{"id":48,"date":"2025-12-13T19:07:52","date_gmt":"2025-12-13T09:07:52","guid":{"rendered":"https:\/\/archive4ones.com\/?p=48"},"modified":"2026-02-16T22:18:14","modified_gmt":"2026-02-16T12:18:14","slug":"year-9-english-reader-story-5","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=48","title":{"rendered":"Year 9 English Reader \u2013 Story 5"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Hello! I\u2019m happy to finish the series with the final story.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The fifth and final story will focus on&nbsp;<strong>Physics (Optics and Acoustics)<\/strong>&nbsp;and how those principles are used in engineering to solve a public safety issue involving a structure.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here is the first chapter of the fifth story.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf09 Story 5: The Resonance Riddle<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 1: The Vibrating Bridge<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"968\" height=\"676\" src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C1.png\" alt=\"\" class=\"wp-image-1583\" srcset=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C1.png 968w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C1-300x210.png 300w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C1-768x536.png 768w\" sizes=\"auto, (max-width: 968px) 100vw, 968px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-1.mp3\"><\/audio><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Liam<\/strong>&nbsp;stood beneath the massive steel arch of the&nbsp;<strong>Cairns Harbour Bridge<\/strong>. The bridge was a vital piece of infrastructure, connecting the northern suburbs to the city centre. He wasn\u2019t there on a tourist trip; he was interning with a team of structural engineers from the&nbsp;<strong>Department of Main Roads<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The air was heavy and humid, and the noise from the traffic above was a constant, loud drone. But there was a new sound that worried the engineers\u2014a low, humming vibration that occasionally intensified into an unsettling&nbsp;<strong>wail<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cWe call it the \u2018singing bridge,\u2019\u201d said&nbsp;<strong>Mr. Hayes<\/strong>, the lead structural engineer, adjusting the safety helmet on his head. \u201cIt\u2019s been happening for about six months now, mostly during peak traffic hours when the bridge is carrying maximum load, or during high winds.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The structural integrity of the bridge was sound\u2014it wasn\u2019t about to collapse. However, the unexpected and excessive vibration indicated a phenomenon known as&nbsp;<strong>resonance<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mr. Hayes explained the physics to Liam. \u201cEvery structure has a&nbsp;<strong>natural frequency<\/strong>\u2014the specific rate at which it will vibrate if disturbed. Think of a guitar string; if you pluck it, it vibrates at its natural note. If an external force, like the wind or the rhythmic pounding of heavy traffic, matches that natural frequency, the vibrations build up rapidly. This is&nbsp;<strong>resonance<\/strong>, and it dramatically amplifies the oscillation.\u201d .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The wailing sound was the acoustic manifestation of the bridge vibrating too strongly. Over time, these excessive oscillations could cause metal fatigue and weaken connections, turning a maintenance issue into a safety crisis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam\u2019s task was to help pinpoint the source of the acoustic feedback. He was given a briefcase containing an advanced piece of equipment: a&nbsp;<strong>Laser Vibrometer<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cThis device uses a laser beam to measure the frequency and amplitude of vibrations on a surface without touching it,\u201d Mr. Hayes explained. \u201cWe need to collect precise&nbsp;<strong>frequency data<\/strong>&nbsp;from different parts of the bridge\u2014the main deck, the central arch, and the support cables\u2014to figure out exactly which section is entering resonance and what frequency is triggering it.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The initial readings were messy. The bridge was vibrating at multiple frequencies simultaneously, thanks to the constant stream of cars, trucks, and buses. Liam knew he had to separate the&nbsp;<strong>signal<\/strong>&nbsp;(the bridge\u2019s natural frequency) from the&nbsp;<strong>noise<\/strong>&nbsp;(the random traffic vibrations). He needed to find the specific&nbsp;<strong>critical frequency<\/strong>&nbsp;that was causing the dangerous wail.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Comprehension Questions (Chapter 1)<\/h3>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-1Q.mp3\"><\/audio><\/figure>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>What is the&nbsp;<strong>main problem<\/strong>&nbsp;concerning the Cairns Harbour Bridge, and what physical event does the wailing sound indicate?<\/li>\n\n\n\n<li>What is a structure\u2019s&nbsp;<strong>natural frequency<\/strong>, and how does it relate to the concept of&nbsp;<strong>resonance<\/strong>?<\/li>\n\n\n\n<li>What are the two specific external forces that Mr. Hayes suspects might be triggering the resonance in the bridge?<\/li>\n\n\n\n<li>What sophisticated piece of&nbsp;<strong>physics equipment<\/strong>&nbsp;was Liam given to help with his task, and what principle does it use to take measurements?<\/li>\n\n\n\n<li>What&nbsp;<strong>main challenge<\/strong>&nbsp;did Liam face when taking initial readings, and what was he trying to identify?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">I will continue the story. Here is Chapter 2 of&nbsp;<strong>Story 5: The Resonance Riddle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf09 Story 5: The Resonance Riddle<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 2: Isolating the Critical Frequency<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"818\" height=\"550\" src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C2.png\" alt=\"\" class=\"wp-image-1584\" srcset=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C2.png 818w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C2-300x202.png 300w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C2-768x516.png 768w\" sizes=\"auto, (max-width: 818px) 100vw, 818px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-2.mp3\"><\/audio><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Liam and Mr. Hayes set up their equipment under the main span of the bridge. The traffic was heavy, creating a chaotic mix of sounds and vibrations. To successfully identify the bridge\u2019s&nbsp;<strong>natural frequency<\/strong>&nbsp;and the external force triggering resonance, Liam needed to use&nbsp;<strong>signal processing<\/strong>&nbsp;principles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cWe can\u2019t rely on the raw, instantaneous data,\u201d Mr. Hayes explained. \u201cThe bridge is like a complex machine with many moving parts. We need to find the&nbsp;<strong>dominant frequency<\/strong>&nbsp;that persists across the whole structure when the \u2018singing\u2019 starts.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam mounted the&nbsp;<strong>Laser Vibrometer<\/strong>&nbsp;at several points along the steel girders. The vibrometer measured the amplitude of vibration in micrometres (mu m) against frequency (in Hertz, Hz). He then input the data into specialised engineering software to perform a&nbsp;<strong>Fast Fourier Transform (FFT)<\/strong>&nbsp;analysis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The FFT is a mathematical process that converts a complex signal (like the bridge\u2019s combined vibration) into its individual component frequencies. .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After analysing several hours of data, a clear pattern emerged. While the traffic noise created a scatter of frequencies, two major&nbsp;<strong>spectral peaks<\/strong>&nbsp;consistently appeared when the bridge began to wail:<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Peak 1:<\/strong>&nbsp;A constant, low-amplitude peak at 1.5 Hz. This was identified as the bridge\u2019s main, stable&nbsp;<strong>natural frequency<\/strong>&nbsp;when under load.<\/li>\n\n\n\n<li><strong>Peak 2:<\/strong>&nbsp;A highly variable, intense peak that spiked between 1.5 Hz and 1.8Hz. This spike corresponded exactly with the onset of the loud, unsettling wail.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cAha,\u201d Mr. Hayes said, reviewing the FFT graph. \u201cThe external force is slightly higher than the natural frequency, but it\u2019s close enough\u2014specifically the 1.8 Hz frequency\u2014to pull the bridge into destructive oscillation.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now they had to identify the source of that 1.8 Hz external frequency. Liam realised that the bridge design included an array of vertical&nbsp;<strong>support cables<\/strong>&nbsp;running from the arch down to the deck.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">He took a new set of readings, aiming the laser vibrometer specifically at the central support cables. When he ran the FFT on the cable data alone, the&nbsp;<strong>1.8 Hz peak<\/strong>&nbsp;was magnified exponentially.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cIt\u2019s the cables,\u201d Liam concluded. \u201cThe rhythmic movement of the wind, or perhaps the \u2018galloping\u2019 effect of the heavy traffic, is causing these specific support cables to oscillate at their own natural frequency of 1.8 Hz.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Because the cables are physically attached to the deck, their vibration acts as the&nbsp;<strong>external driving force<\/strong>. When the cables\u2019 1.8 Hz frequency aligns with the bridge\u2019s 1.5 Hz natural frequency, it creates a forced, unstable vibration, leading to the dangerous resonance and the signature wailing sound.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The solution would not be to strengthen the whole bridge, but to focus on cancelling the 1.8 Hz vibration in the cables themselves.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Comprehension Questions (Chapter 2)<\/h3>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-2Q.mp3\"><\/audio><\/figure>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>What is&nbsp;<strong>Fast Fourier Transform (FFT)<\/strong>, and what purpose did Liam use it for in his analysis?<\/li>\n\n\n\n<li>What were the two major&nbsp;<strong>spectral peaks<\/strong>&nbsp;that consistently appeared in the vibration data?<\/li>\n\n\n\n<li>Which of the two peaks represented the bridge\u2019s&nbsp;<strong>stable natural frequency<\/strong>?<\/li>\n\n\n\n<li>What specific part of the bridge did Liam focus on in his second round of readings, and why did this area show an exponential magnification of the 1.8 Hz frequency?<\/li>\n\n\n\n<li>Based on the physics, what did Liam conclude was acting as the&nbsp;<strong>external driving force<\/strong>&nbsp;causing the resonance?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">I will continue the story. Here is Chapter 3 of&nbsp;<strong>Story 5: The Resonance Riddle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf09 Story 5: The Resonance Riddle<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 3: Damping the Driver<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"566\" height=\"396\" src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C3.png\" alt=\"\" class=\"wp-image-1586\" srcset=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C3.png 566w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C3-300x210.png 300w\" sizes=\"auto, (max-width: 566px) 100vw, 566px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-3.mp3\"><\/audio><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Having identified the source of the dangerous&nbsp;<strong>resonance<\/strong>&nbsp;as the vertical&nbsp;<strong>support cables<\/strong>&nbsp;oscillating at 1.8 Hz, the engineering team\u2019s focus shifted from diagnosis to solution. The problem was an external force (1.8 Hz from the cables) matching the bridge\u2019s natural frequency (1.5 Hz). To fix it, they needed to change the physics of the system.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cWe have two options,\u201d Mr. Hayes explained to Liam. \u201cWe can change the bridge\u2019s&nbsp;<strong>natural frequency<\/strong>\u2014which would mean major structural reinforcement and massive cost\u2014or we can eliminate the&nbsp;<strong>external driving force<\/strong>&nbsp;from the cables.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">They chose the latter. The core principle of their solution was&nbsp;<strong>damping<\/strong>. Damping is the process of dissipating (converting) mechanical energy (vibration) into another form of energy, usually heat. .<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The specific device they planned to use was a&nbsp;<strong>Tuned Mass Damper (TMD)<\/strong>, or more simply, a dampener, which would be installed on each problematic support cable.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A TMD is essentially a weight attached to the structure by a spring and a viscous fluid (like oil or silicone). It is meticulously engineered to oscillate at the same frequency as the unwanted vibration\u2014in this case, 1.8 Hz.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cThe beauty of the TMD,\u201d Mr. Hayes said, \u201cis that when the cable starts vibrating at 1.8 Hz, the TMD vibrates&nbsp;<em>out of phase<\/em>&nbsp;with it. The TMD absorbs the cable\u2019s energy, converting that vibrational energy into heat through the viscous fluid, effectively&nbsp;<strong>cancelling out<\/strong>&nbsp;the oscillation before it can be transferred to the main bridge deck.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam\u2019s new task was to assist the engineering team in precisely calculating the required&nbsp;<strong>mass (m)<\/strong>&nbsp;and&nbsp;<strong>spring constant (k)<\/strong>&nbsp;for each TMD. The calculation had to be exact, as the TMD\u2019s frequency must precisely match the cable\u2019s frequency (1.8  Hz. The fundamental frequency of a simple mass-spring system is given by:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">                                                                 <math data-latex=\"f = \\frac{1}{2\\pi} \\sqrt{\\frac{k}{m}}\"><semantics><mrow><mi>f<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><msqrt><mfrac><mi>k<\/mi><mi>m<\/mi><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\">f = \\frac{1}{2\\pi} \\sqrt{\\frac{k}{m}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">They determined that a 50 kg mass, combined with a specific spring constant, was the optimal balance between effectiveness and weight.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The installation phase began over the next two nights, during periods of low traffic. Crews carefully attached the TMD units near the base of the most active support cables. Liam supervised the installation, ensuring the alignment and tension of the TMD springs were set according to the calculated specifications.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As the final dampener was secured, a large gust of wind swept under the bridge. The cables began to hum, but instead of the vibration building up into the familiar, dangerous wail, the sound was muffled, and the oscillation quickly decayed back to silence. The TMDs were doing their job, absorbing the kinetic energy and stopping the resonance before it could take hold.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Comprehension Questions (Chapter 3)<\/h3>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-3Q.mp3\"><\/audio><\/figure>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>What two options did the engineers consider for solving the resonance problem, and which one did they choose?<\/li>\n\n\n\n<li>What is the physics definition of&nbsp;<strong>damping<\/strong>?<\/li>\n\n\n\n<li>What specific device was chosen to eliminate the unwanted vibration, and what is its primary mechanism of action?<\/li>\n\n\n\n<li>Explain the key principle of how a&nbsp;<strong>Tuned Mass Damper (TMD)<\/strong>&nbsp;works to&nbsp;<em>cancel out<\/em>&nbsp;the vibration.<\/li>\n\n\n\n<li>What was the purpose of the&nbsp;<strong>equation<\/strong>&nbsp;in this chapter, and what two variables did Liam need to precisely calculate for the TMD?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">I will continue the story. Here is Chapter 4 of&nbsp;<strong>Story 5: The Resonance Riddle<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf09 Story 5: The Resonance Riddle<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 4: The Sound of Silence<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"987\" height=\"530\" src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C4.png\" alt=\"\" class=\"wp-image-1587\" srcset=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C4.png 987w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C4-300x161.png 300w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C4-768x412.png 768w\" sizes=\"auto, (max-width: 987px) 100vw, 987px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-4.mp3\"><\/audio><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">With the&nbsp;<strong>Tuned Mass Dampers (TMDs)<\/strong>&nbsp;installed on the most active support cables, the engineering team waited for the next major period of high traffic or strong wind to test their solution. This test would be the real-world validation of their theoretical physics calculations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam and Mr. Hayes set up the&nbsp;<strong>Laser Vibrometer<\/strong>&nbsp;in the control room, pointing its sensor at a specific spot on the main deck that had previously shown the highest&nbsp;<strong>amplitude<\/strong>&nbsp;during resonance events. They were ready to use the&nbsp;<strong>Fast Fourier Transform (FFT)<\/strong>&nbsp;analysis one last time to compare the \u2018before\u2019 and \u2018after\u2019 data.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The wind picked up, gusting to 40 km\/h\u2014exactly the condition that had previously triggered the dangerous wail.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On the screen, the raw vibration data showed the bridge moving. However, when Liam ran the&nbsp;<strong>FFT analysis<\/strong>, the graph was dramatically different from the previous week\u2019s results.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The massive, variable peak between 1.5 Hz and 1.8 Hz had almost vanished. It was replaced by a small, stable peak right at the bridge\u2019s natural frequency of 1.5 Hz, but the oscillation amplitude was reduced by over 90%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cThe TMDs worked,\u201d Mr. Hayes announced, relief evident in his voice. \u201cThe&nbsp;<strong>external driving force<\/strong>&nbsp;is gone.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">However, they noticed a new, unexpected, and subtle spectral peak in the analysis: a tiny, consistent spike at 3.0 Hz. It was far from the critical 1.5 Hz and posed no immediate threat, but it was a new vibration.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cWhat\u2019s 3.0 Hz?\u201d Liam wondered, running a quick check of the bridge\u2019s structural harmonics.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mr. Hayes pulled up the bridge blueprints. \u201cThat is exactly the&nbsp;<strong>first harmonic frequency<\/strong>&nbsp;of the central steel arch. It\u2019s the frequency the arch would vibrate at if it were moving in a simpler, faster mode. It\u2019s too high to resonate with the deck, but why is it showing up now?\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">They left the control room and went out onto the deck. The familiar wail was absent, replaced only by the normal rumble of traffic. But as a heavy semi-trailer crossed the main span, Liam noticed a shimmer\u2014a&nbsp;<strong>visual distortion<\/strong>\u2014in the air just above the traffic barriers.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">He aimed the&nbsp;<strong>Laser Vibrometer<\/strong>&nbsp;at the steel barrier itself. The FFT spiked directly at the 3.0 Hz mark. The barrier, which was a long, hollow tube running the length of the deck, was now resonating.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam suddenly recalled a concept from optics:&nbsp;<strong>acoustic refraction<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cThe barrier isn\u2019t vibrating from the wind or traffic,\u201d Liam hypothesised. \u201cIt\u2019s vibrating from&nbsp;<strong>sound<\/strong>! When the bridge was \u2018singing\u2019 at 1.8 Hz, that massive sound energy drowned out all other frequencies. Now that the main wail is gone, the 3.0 Hz sound waves created by the low-frequency rumble of heavy diesel engines are resonating with the thin, hollow steel of the barrier.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This was a classic&nbsp;<strong>acoustics problem<\/strong>, not a structural one. The TMDs had fixed the major structural issue, only to reveal a minor acoustic one hidden beneath the roar. They had achieved structural silence, but the&nbsp;<strong>physics of sound<\/strong>&nbsp;was now creating a small, new disturbance.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Comprehension Questions (Chapter 4)<\/h3>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-4Q.mp3\"><\/audio><\/figure>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>How did the&nbsp;<strong>FFT analysis<\/strong>&nbsp;of the bridge vibration change after the TMDs were installed?<\/li>\n\n\n\n<li>What new, unexpected spectral peak appeared in the analysis, and what part of the bridge structure did it correspond to?<\/li>\n\n\n\n<li>Why did this new peak&nbsp;<em>not<\/em>&nbsp;pose an immediate threat to the bridge\u2019s structural integrity?<\/li>\n\n\n\n<li>What physical phenomenon (related to light\/sound) did Liam recall that might explain the new vibration in the traffic barrier?<\/li>\n\n\n\n<li>What was Liam\u2019s&nbsp;<strong>final hypothesis<\/strong>&nbsp;about the source of the 3.0 Hz vibration, and why did it only appear&nbsp;<em>after<\/em>&nbsp;the main resonance problem was solved?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">I will continue the story. Here is Chapter 5 of&nbsp;<strong>Story 5: The Resonance Riddle<\/strong>, concluding the final story.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83c\udf09 Story 5: The Resonance Riddle<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Chapter 5: Silence and Stability<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"999\" height=\"673\" src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C5.png\" alt=\"\" class=\"wp-image-1588\" srcset=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C5.png 999w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C5-300x202.png 300w, https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Y9-S5-C5-768x517.png 768w\" sizes=\"auto, (max-width: 999px) 100vw, 999px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-5.mp3\"><\/audio><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The successful installation of the&nbsp;<strong>Tuned Mass Dampers (TMDs)<\/strong>&nbsp;had secured the Cairns Harbour Bridge from the dangerous 1.8 Hz structural resonance. The structural safety crisis was averted, thanks to the application of&nbsp;<strong>vibrational physics<\/strong>&nbsp;and precise engineering.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The only remaining issue was the subtle, newly revealed acoustic resonance in the long, hollow steel&nbsp;<strong>traffic barriers<\/strong>&nbsp;at 3.0 Hz. While not a structural threat, the sustained low hum could be irritating to drivers and eventually lead to cosmetic fatigue in the barriers themselves.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam and Mr. Hayes knew they couldn\u2019t use another expensive TMD system for the barrier. The solution had to be simple and cheap, targeting the&nbsp;<strong>acoustics<\/strong>&nbsp;and&nbsp;<strong>material physics<\/strong>&nbsp;of the thin steel tube.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cWe need to change the barrier\u2019s&nbsp;<strong>natural acoustic frequency<\/strong>&nbsp;so it no longer matches the 3.0 Hz sound wave from the heavy diesel engines,\u201d Mr. Hayes suggested.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The easiest way to alter a hollow object\u2019s resonance frequency is to change its&nbsp;<strong>mass<\/strong>&nbsp;or its&nbsp;<strong>internal damping coefficient<\/strong>. They settled on increasing the damping, which would absorb the sound energy.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The final, elegant solution involved&nbsp;<strong>acoustic filling<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The maintenance crew pumped a cheap, inert material\u2014a fine, compacted sand\u2014into the hollow interior of the steel barriers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Result 1: Increased Mass:<\/strong>&nbsp;The sand slightly increased the barrier\u2019s&nbsp;<strong>mass<\/strong>, which lowered its natural frequency below 3.0 Hz.<\/li>\n\n\n\n<li><strong>Result 2: Internal Damping:<\/strong>&nbsp;More importantly, the loose sand granules provided immense&nbsp;<strong>internal damping<\/strong>. When the steel tube was struck by the 3.0 Hz sound wave, the energy was instantly transferred to the trillions of tiny grains of sand, which rub against each other, converting the sound vibration into negligible heat. This process instantly disrupted the barrier\u2019s ability to sustain a resonant frequency.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Liam once again used the&nbsp;<strong>Laser Vibrometer<\/strong>&nbsp;to take the final readings. With the sand filling in place, the 3.0 Hz peak in the FFT graph vanished entirely. The bridge was finally silent, with the only noticeable sound being the normal rumble of traffic.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The project had been a perfect demonstration of applied science: they had used&nbsp;<strong>optics<\/strong>&nbsp;(Laser Vibrometer) and&nbsp;<strong>signal processing<\/strong>&nbsp;(FFT) to diagnose a&nbsp;<strong>vibrational physics<\/strong>&nbsp;problem (resonance), and solved it first with complex&nbsp;<strong>mechanical engineering<\/strong>&nbsp;(TMDs), and then with simple&nbsp;<strong>material science<\/strong>&nbsp;(sand damping).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mr. Hayes shook Liam\u2019s hand. \u201cYou didn\u2019t just help install dampeners, Liam. You helped us understand the fundamental physics that governs massive structures. The \u2018singing bridge\u2019 is silent, and it\u2019s safer, because you knew how to look beyond the noise and find the critical frequency.\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Liam felt a sense of immense achievement. He had learned that the equations and concepts taught in his Year 9 physics class\u2014like natural frequency, resonance, and damping\u2014were the literal tools that keep the world\u2019s most vital structures stable and safe. The safety of thousands of commuters depended on the accuracy of his FFT analysis.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Comprehension Questions (Chapter 5)<\/h3>\n\n\n\n<figure class=\"wp-block-audio\"><audio controls src=\"https:\/\/archive4ones.com\/2ndstudy\/wp-content\/uploads\/sites\/8\/2025\/12\/Year9-5-5Q.mp3\"><\/audio><\/figure>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li>What two specific&nbsp;<strong>material properties<\/strong>&nbsp;did the engineers decide to change to solve the barrier resonance problem?<\/li>\n\n\n\n<li>What simple, low-cost material did the maintenance crew use for the&nbsp;<strong>acoustic filling<\/strong>?<\/li>\n\n\n\n<li>Explain the two ways the acoustic filling material helped solve the resonance problem based on the principles of&nbsp;<strong>physics and materials science<\/strong>.<\/li>\n\n\n\n<li>What two specific&nbsp;<strong>tools\/techniques<\/strong>&nbsp;(from physics or data) were used to confirm that the 3.0 Hz vibration had been eliminated?<\/li>\n\n\n\n<li>What was the biggest&nbsp;<strong>takeaway lesson<\/strong>&nbsp;Liam learned about the connection between physics concepts and structural engineering?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">That concludes the fifth and final five-chapter story,&nbsp;<strong>The Resonance Riddle<\/strong>, and completes the requested set of five reading practice stories.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Is there anything else I can help you with today, perhaps reviewing the comprehension questions or summarising the core science concepts from all five stories?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">****************************************************************************<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b2c5\u8a71\u3001\u305d\u3057\u3066\u6700\u5f8c\u306e\u8a71\u3067\u306f\u3001\u7269\u7406\u5b66\uff08\u5149\u5b66\u3068\u97f3\u97ff\uff09\u3068\u3001\u305d\u308c\u3089\u306e\u539f\u7406\u304c\u69cb\u9020\u7269\u306b\u95a2\u308f\u308b\u516c\u5171\u5b89\u5168\u554f\u984c\u306e\u89e3\u6c7a\u306b\u5de5\u5b66\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u5fdc\u7528\u3055\u308c\u3066\u3044\u308b\u304b\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b2c5\u8a71\uff1a\u5171\u9cf4\u306e\u8b0e<br>\u7b2c1\u7ae0\uff1a\u632f\u52d5\u3059\u308b\u6a4b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30a2\u30e0\u306f\u30b1\u30a2\u30f3\u30ba\u30fb\u30cf\u30fc\u30d0\u30fc\u30fb\u30d6\u30ea\u30c3\u30b8\u306e\u5de8\u5927\u306a\u92fc\u9244\u30a2\u30fc\u30c1\u306e\u4e0b\u306b\u7acb\u3063\u3066\u3044\u307e\u3057\u305f\u3002\u3053\u306e\u6a4b\u306f\u5317\u90e8\u90ca\u5916\u3068\u5e02\u5185\u4e2d\u5fc3\u90e8\u3092\u7d50\u3076\u91cd\u8981\u306a\u30a4\u30f3\u30d5\u30e9\u3067\u3059\u3002\u5f7c\u306f\u89b3\u5149\u65c5\u884c\u3067\u3053\u3053\u306b\u6765\u305f\u306e\u3067\u306f\u306a\u304f\u3001\u4e3b\u8981\u9053\u8def\u5c40\u306e\u69cb\u9020\u30a8\u30f3\u30b8\u30cb\u30a2\u30c1\u30fc\u30e0\u3067\u30a4\u30f3\u30bf\u30fc\u30f3\u30b7\u30c3\u30d7\u3092\u3057\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7a7a\u6c17\u306f\u91cd\u304f\u6e7f\u3063\u307d\u304f\u3001\u4e0a\u7a7a\u306e\u4ea4\u901a\u9a12\u97f3\u306f\u7d76\u3048\u9593\u306a\u304f\u5927\u304d\u306a\u5358\u8abf\u306a\u97f3\u3067\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30a8\u30f3\u30b8\u30cb\u30a2\u305f\u3061\u3092\u60a9\u307e\u305b\u308b\u65b0\u305f\u306a\u97f3\u304c\u805e\u3053\u3048\u3066\u304d\u307e\u3057\u305f\u3002\u305d\u308c\u306f\u3001\u4f4e\u304f\u3046\u306a\u308a\u58f0\u306e\u3088\u3046\u306a\u632f\u52d5\u3067\u3001\u6642\u6298\u3001\u4e0d\u5b89\u306a\u60b2\u9cf4\u3078\u3068\u5f37\u307e\u308b\u3082\u306e\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u79c1\u305f\u3061\u306f\u3053\u308c\u3092\u300e\u6b4c\u3046\u6a4b\u300f\u3068\u547c\u3093\u3067\u3044\u307e\u3059\u300d\u3068\u3001\u4e3b\u4efb\u69cb\u9020\u30a8\u30f3\u30b8\u30cb\u30a2\u306e\u30d8\u30a4\u30ba\u6c0f\u306f\u5b89\u5168\u30d8\u30eb\u30e1\u30c3\u30c8\u3092\u8abf\u6574\u3057\u306a\u304c\u3089\u8a00\u3063\u305f\u3002\u300c\u3082\u30466\u30f6\u6708\u307b\u3069\u524d\u304b\u3089\u3001\u4e3b\u306b\u4ea4\u901a\u91cf\u304c\u591a\u304f\u6a4b\u306b\u6700\u5927\u8377\u91cd\u304c\u304b\u304b\u308b\u6642\u9593\u5e2f\u3084\u5f37\u98a8\u6642\u306b\u767a\u751f\u3057\u3066\u3044\u307e\u3059\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6a4b\u306e\u69cb\u9020\u7684\u5b8c\u5168\u6027\u306f\u826f\u597d\u3067\u3001\u5d29\u843d\u5bf8\u524d\u3067\u306f\u306a\u304b\u3063\u305f\u3002\u3057\u304b\u3057\u3001\u4e88\u671f\u305b\u306c\u904e\u5ea6\u306e\u632f\u52d5\u306f\u3001\u5171\u632f\u3068\u547c\u3070\u308c\u308b\u73fe\u8c61\u3092\u793a\u5506\u3057\u3066\u3044\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d8\u30a4\u30ba\u6c0f\u306f\u30ea\u30a2\u30e0\u306b\u305d\u306e\u7269\u7406\u7684\u6027\u8cea\u3092\u8aac\u660e\u3057\u305f\u3002\u300c\u3059\u3079\u3066\u306e\u69cb\u9020\u7269\u306b\u306f\u56fa\u6709\u632f\u52d5\u6570\u3001\u3064\u307e\u308a\u4e71\u308c\u305f\u5834\u5408\u306b\u632f\u52d5\u3059\u308b\u7279\u5b9a\u306e\u901f\u5ea6\u304c\u3042\u308a\u307e\u3059\u3002\u30ae\u30bf\u30fc\u306e\u5f26\u3092\u60f3\u50cf\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\u5f26\u3092\u5f3e\u304f\u3068\u3001\u672c\u6765\u306e\u97f3\u3067\u632f\u52d5\u3057\u307e\u3059\u3002\u98a8\u3084\u4ea4\u901a\u91cf\u306e\u591a\u3044\u9053\u8def\u306e\u30ea\u30ba\u30df\u30ab\u30eb\u306a\u885d\u6483\u306a\u3069\u306e\u5916\u529b\u304c\u3053\u306e\u56fa\u6709\u632f\u52d5\u6570\u3068\u4e00\u81f4\u3059\u308b\u3068\u3001\u632f\u52d5\u306f\u6025\u901f\u306b\u5897\u5927\u3057\u307e\u3059\u3002\u3053\u308c\u304c\u5171\u632f\u3067\u3042\u308a\u3001\u632f\u52d5\u304c\u5287\u7684\u306b\u5897\u5e45\u3055\u308c\u307e\u3059\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3042\u306e\u60b2\u9cf4\u306e\u3088\u3046\u306a\u97f3\u306f\u3001\u6a4b\u304c\u904e\u5ea6\u306b\u632f\u52d5\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u97f3\u97ff\u7684\u306b\u8868\u3057\u3066\u3044\u305f\u3002\u6642\u9593\u304c\u7d4c\u3064\u306b\u3064\u308c\u3066\u3001\u3053\u3046\u3057\u305f\u904e\u5270\u306a\u632f\u52d5\u306f\u91d1\u5c5e\u75b2\u52b4\u3092\u5f15\u304d\u8d77\u3053\u3057\u3001\u63a5\u5408\u90e8\u3092\u5f31\u3081\u3001\u30e1\u30f3\u30c6\u30ca\u30f3\u30b9\u306e\u554f\u984c\u3092\u5b89\u5168\u4e0a\u306e\u5371\u6a5f\u3078\u3068\u767a\u5c55\u3055\u305b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30a2\u30e0\u306e\u4efb\u52d9\u306f\u3001\u97f3\u97ff\u30d5\u30a3\u30fc\u30c9\u30d0\u30c3\u30af\u306e\u767a\u751f\u6e90\u3092\u7279\u5b9a\u3059\u308b\u3053\u3068\u3067\u3057\u305f\u3002\u5f7c\u306b\u306f\u3001\u30ec\u30fc\u30b6\u30fc\u632f\u52d5\u8a08\u3068\u3044\u3046\u9ad8\u5ea6\u306a\u6a5f\u5668\u304c\u5165\u3063\u305f\u30d6\u30ea\u30fc\u30d5\u30b1\u30fc\u30b9\u304c\u6e21\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p 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class=\"wp-block-paragraph\">TMD\u306f\u57fa\u672c\u7684\u306b\u3001\u30d0\u30cd\u3068\u7c98\u6027\u6d41\u4f53\uff08\u30aa\u30a4\u30eb\u3084\u30b7\u30ea\u30b3\u30f3\u306a\u3069\uff09\u306b\u3088\u3063\u3066\u69cb\u9020\u7269\u306b\u53d6\u308a\u4ed8\u3051\u3089\u308c\u305f\u91cd\u308a\u3067\u3059\u3002\u3053\u306e\u632f\u52d5\u5b50\u306f\u3001\u4e0d\u8981\u306a\u632f\u52d5\u3068\u540c\u3058\u5468\u6ce2\u6570\uff08\u3053\u306e\u5834\u5408\u306f1.8Hz\uff09\u3067\u632f\u52d5\u3059\u308b\u3088\u3046\u306b\u3001\u7d30\u5fc3\u306e\u6ce8\u610f\u3092\u6255\u3063\u3066\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30d8\u30a4\u30ba\u6c0f\u306f\u3001\u300cTMD\u306e\u512a\u308c\u305f\u70b9\u306f\u3001\u30b1\u30fc\u30d6\u30eb\u304c1.8Hz\u3067\u632f\u52d5\u3057\u59cb\u3081\u308b\u3068\u3001TMD\u304c\u305d\u308c\u3068\u4f4d\u76f8\u304c\u305a\u308c\u3066\u632f\u52d5\u3059\u308b\u3053\u3068\u3067\u3059\u3002TMD\u306f\u30b1\u30fc\u30d6\u30eb\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u5438\u53ce\u3057\u3001\u7c98\u6027\u6d41\u4f53\u3092\u901a\u3057\u3066\u305d\u306e\u632f\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u71b1\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u3001\u632f\u52d5\u304c\u6a4b\u306e\u4e3b\u5e8a\u7248\u306b\u4f1d\u308f\u308b\u524d\u306b\u52b9\u679c\u7684\u306b\u6253\u3061\u6d88\u3057\u307e\u3059\u300d\u3068\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30a2\u30e0\u306e\u65b0\u305f\u306a\u4efb\u52d9\u306f\u3001\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\u30c1\u30fc\u30e0\u304c\u5404TMD\u306b\u5fc5\u8981\u306a\u8cea\u91cf\uff08m\uff09\u3068\u30d0\u30cd\u5b9a\u6570\uff08k\uff09\u3092\u6b63\u78ba\u306b\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u652f\u63f4\u3059\u308b\u3053\u3068\u3067\u3057\u305f\u3002 TMD\u306e\u5468\u6ce2\u6570\u306f\u30b1\u30fc\u30d6\u30eb\u306e\u5468\u6ce2\u6570\uff081.8Hz\uff09\u3068\u6b63\u78ba\u306b\u4e00\u81f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u8a08\u7b97\u306f\u6b63\u78ba\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002\u5358\u7d14\u306a\u8cea\u91cf\u30d0\u30cd\u30b7\u30b9\u30c6\u30e0\u306e\u57fa\u672c\u5468\u6ce2\u6570\u306f\u3001\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f = <math data-latex=\" \\frac{1}{2\\pi} \\sqrt{\\frac{k}{m}}\"><semantics><mrow><mfrac><mn>1<\/mn><mrow><mn>2<\/mn><mi>\u03c0<\/mi><\/mrow><\/mfrac><msqrt><mfrac><mi>k<\/mi><mi>m<\/mi><\/mfrac><\/msqrt><\/mrow><annotation encoding=\"application\/x-tex\"> \\frac{1}{2\\pi} \\sqrt{\\frac{k}{m}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f7c\u3089\u306f\u300150kg\u306e\u8cea\u91cf\u3068\u7279\u5b9a\u306e\u30d0\u30cd\u5b9a\u6570\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u52b9\u679c\u3068\u91cd\u91cf\u306e\u6700\u9069\u306a\u30d0\u30e9\u30f3\u30b9\u304c\u5f97\u3089\u308c\u308b\u3068\u5224\u65ad\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8a2d\u7f6e\u4f5c\u696d\u306f\u3001\u4ea4\u901a\u91cf\u306e\u5c11\u306a\u30442\u6669\u306b\u308f\u305f\u3063\u3066\u958b\u59cb\u3055\u308c\u307e\u3057\u305f\u3002\u4f5c\u696d\u54e1\u306f\u3001\u6700\u3082\u6d3b\u767a\u306a\u652f\u6301\u30b1\u30fc\u30d6\u30eb\u306e\u6839\u5143\u4ed8\u8fd1\u306bTMD\u30e6\u30cb\u30c3\u30c8\u3092\u614e\u91cd\u306b\u53d6\u308a\u4ed8\u3051\u307e\u3057\u305f\u3002\u30ea\u30a2\u30e0\u306f\u8a2d\u7f6e\u3092\u76e3\u7763\u3057\u3001TMD\u30d0\u30cd\u306e\u914d\u7f6e\u3068\u5f35\u529b\u304c\u8a08\u7b97\u3055\u308c\u305f\u4ed5\u69d8\u901a\u308a\u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u5f8c\u306e\u30c0\u30f3\u30d1\u30fc\u304c\u56fa\u5b9a\u3055\u308c\u308b\u3068\u3001\u5f37\u3044\u7a81\u98a8\u304c\u6a4b\u306e\u4e0b\u3092\u5439\u304d\u629c\u3051\u307e\u3057\u305f\u3002\u30b1\u30fc\u30d6\u30eb\u306f\u3046\u306a\u308a\u97f3\u3092\u7acb\u3066\u59cb\u3081\u307e\u3057\u305f\u304c\u3001\u632f\u52d5\u304c\u304a\u306a\u3058\u307f\u306e\u5371\u967a\u306a\u97f3\u306b\u307e\u3067\u5897\u5e45\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u97f3\u306f\u6291\u3048\u3089\u308c\u3001\u632f\u52d5\u306f\u3059\u3050\u306b\u9759\u5bc2\u306b\u623b\u308a\u307e\u3057\u305f\u3002TMD\u306f\u4ed5\u4e8b\u306f\u3001\u904b\u52d5\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u5438\u53ce\u3057\u3001\u5171\u9cf4\u304c\u5b9a\u7740\u3059\u308b\u524d\u306b\u305d\u308c\u3092\u6b62\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b2c4\u7ae0\uff1a\u9759\u5bc2\u306e\u97f3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6700\u3082\u6d3b\u767a\u306a\u652f\u6301\u30b1\u30fc\u30d6\u30eb\u306b\u540c\u8abf\u8cea\u91cf\u30c0\u30f3\u30d1\u30fc\uff08TMD\uff09\u3092\u8a2d\u7f6e\u3057\u305f\u5f8c\u3001\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\u30c1\u30fc\u30e0\u306f\u3001\u6b21\u306b\u4ea4\u901a\u91cf\u304c\u591a\u304f\u306a\u308b\u6642\u671f\u3084\u5f37\u98a8\u306b\u306a\u308b\u6642\u671f\u3092\u5f85\u3061\u3001\u89e3\u6c7a\u7b56\u3092\u30c6\u30b9\u30c8\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u30c6\u30b9\u30c8\u306f\u3001\u7406\u8ad6\u7269\u7406\u5b66\u306e\u8a08\u7b97\u7d50\u679c\u3092\u73fe\u5b9f\u4e16\u754c\u3067\u691c\u8a3c\u3059\u308b\u3082\u306e\u3067\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30ea\u30a2\u30e0\u3068\u30d8\u30a4\u30ba\u6c0f\u306f\u5236\u5fa1\u5ba4\u306b\u30ec\u30fc\u30b6\u30fc\u632f\u52d5\u8a08\u3092\u8a2d\u7f6e\u3057\u3001\u305d\u306e\u30bb\u30f3\u30b5\u30fc\u3092\u30e1\u30a4\u30f3\u30c7\u30c3\u30ad\u4e0a\u306e\u7279\u5b9a\u306e\u5730\u70b9\u306b\u5411\u3051\u307e\u3057\u305f\u3002\u3053\u306e\u5730\u70b9\u306f\u3001\u4ee5\u524d\u5171\u632f\u73fe\u8c61\u306e\u969b\u306b\u6700\u3082\u9ad8\u3044\u632f\u5e45\u3092\u793a\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u5f7c\u3089\u306f\u3001\u6700\u5f8c\u306b\u3082\u3046\u4e00\u5ea6\u9ad8\u901f\u30d5\u30fc\u30ea\u30a8\u5909\u63db\uff08FFT\uff09\u89e3\u6790\u3092\u884c\u3044\u3001\u300c\u524d\u300d\u3068\u300c\u5f8c\u300d\u306e\u30c7\u30fc\u30bf\u3092\u6bd4\u8f03\u3059\u308b\u6e96\u5099\u3092\u6574\u3048\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u98a8\u304c\u5f37\u307e\u308a\u3001\u7a81\u98a8\u304c\u6642\u901f40\u30ad\u30ed\u30e1\u30fc\u30c8\u30eb\u306b\u9054\u3057\u307e\u3057\u305f\u3002\u307e\u3055\u306b\u3001\u4ee5\u524d\u5371\u967a\u306a\u97f3\u3092\u5f15\u304d\u8d77\u3053\u3057\u305f\u72b6\u6cc1\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u753b\u9762\u4e0a\u306e\u751f\u306e\u632f\u52d5\u30c7\u30fc\u30bf\u3067\u306f\u3001\u6a4b\u304c\u52d5\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30ea\u30a2\u30e0\u304cFFT\u89e3\u6790\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u30b0\u30e9\u30d5\u306f\u524d\u9031\u306e\u7d50\u679c\u3068\u306f\u5287\u7684\u306b\u7570\u306a\u3063\u3066\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1.5Hz\u304b\u30891.8Hz\u306e\u9593\u306e\u5927\u304d\u304f\u5909\u52d5\u3059\u308b\u30d4\u30fc\u30af\u306f\u307b\u307c\u6d88\u6ec5\u3057\u3001\u6a4b\u306e\u56fa\u6709\u632f\u52d5\u6570\u3067\u3042\u308b1.5Hz\u306b\u5c0f\u3055\u304f\u5b89\u5b9a\u3057\u305f\u30d4\u30fc\u30af\u304c\u73fe\u308c\u305f\u3002\u3057\u304b\u3057\u3001\u632f\u52d5\u632f\u5e45\u306f90%\u4ee5\u4e0a\u6e1b\u5c11\u3057\u3066\u3044\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300cTMD\u306f\u6a5f\u80fd\u3057\u307e\u3057\u305f\u300d\u3068\u30d8\u30a4\u30ba\u6c0f\u306f\u58f0\u306b\u5b89\u5835\u306e\u8272\u304c\u306b\u3058\u307f\u51fa\u3066\u3044\u305f\u3002\u300c\u5916\u90e8\u99c6\u52d5\u529b\u306f\u306a\u304f\u306a\u308a\u307e\u3057\u305f\u3002\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u5206\u6790\u306e\u7d50\u679c\u3001\u65b0\u305f\u306a\u3001\u4e88\u671f\u305b\u306c\u3001\u305d\u3057\u3066\u5fae\u5999\u306a\u30b9\u30da\u30af\u30c8\u30eb\u30d4\u30fc\u30af\u304c\u898b\u3064\u304b\u3063\u305f\u30023.0Hz\u306b\u5c0f\u3055\u306a\u3001\u3057\u304b\u3057\u4e00\u8cab\u3057\u305f\u30b9\u30d1\u30a4\u30af\u304c\u898b\u3089\u308c\u308b\u306e\u3060\u3002\u3053\u308c\u306f\u5371\u967a\u306a1.5Hz\u304b\u3089\u306f\u7a0b\u9060\u304f\u3001\u76f4\u3061\u306b\u8105\u5a01\u3068\u306a\u308b\u3088\u3046\u306a\u3082\u306e\u3067\u306f\u306a\u3044\u304c\u3001\u65b0\u305f\u306a\u632f\u52d5\u3060\u3063\u305f\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c3.0Hz\u3063\u3066\u4f55\uff1f\u300d\u30ea\u30a2\u30e0\u306f\u6a4b\u306e\u69cb\u9020\u8abf\u548c\u632f\u52d5\u3092\u7d20\u65e9\u304f\u78ba\u8a8d\u3057\u306a\u304c\u3089\u3001\u7591\u554f\u306b\u601d\u3063\u305f\u3002<\/p>\n\n\n\n<p 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I\u2019m happy to finish the series with the final story. The fifth and final story will focus on&nbsp;Physics (Optics and Acoustics)&nbsp;and how those principles are used in engineering to solve a public safety issue involving a structure. Here is the first chapter of the fifth story. \ud83c\udf09 Story 5: The Resonance Riddle Chapter 1: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-48","post","type-post","status-publish","format-standard","hentry","category-jr-english"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/48","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=48"}],"version-history":[{"count":5,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/48\/revisions"}],"predecessor-version":[{"id":1589,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/48\/revisions\/1589"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=48"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=48"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}