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$\bullet$ (a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern having the same frequency of the note that is sung. If someone sings the note $B$ flat that has a frequency of 466 $\mathrm{Hz}$ , how much time does it take the person's vocal cords to vibrate through one complete cycle, and what is the angular frequency of the cords? (b) Hearing. When sound waves strike the eardrum, this membrane vibrates with the same frequency as the sound. The highest pitch that typical humans can hear has a period of 50.0$\mu \mathrm{s} .$ What are the frequency and angular frequency of the vibrating eardrum for this sound? (c) Vision. When light having vibrations with angular frequency ranging from $2.7 \times 10^{15} \mathrm{rad} / \mathrm{s}$ to $4.7 \times 10^{15} \mathrm{rad} / \mathrm{s}$ strikes the retina of the eye, it stimulates the receptor cells there and is perceived as visible light. What are the limits of the period and frequency of this light? (d) Ultrasound. High-frequency sound waves (ultrasound) are used to probe the interior of the body, much as x rays do. To detect a small objects such as tumors, a frequency of around 5.0 $\mathrm{MHz}$ is used. What are the period and angular frequency of the molecular vibrations caused by this pulse of sound?

a) $2.15 \times 10^{-3} \mathrm{s}$$2.93 \times 10^{3} \mathrm{rad} / \mathrm{s}$b) $2 \times 10^{4} \mathrm{Hz}$$1.26 \times 10^{5} \mathrm{rad} / \mathrm{s}$c) $1.34 \times 10^{-15} \mathrm{s}$ to $2.32 \times 10^{-15} \mathrm{s}$$4.30 \times 10^{14} \mathrm{Hz}$ to $7.48 \times 10^{14} \mathrm{Hz}$d) $2 \times 10^{-7} \mathrm{s}$$3.14 \times 10^{7} \mathrm{Hz}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

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Okay, So for the first question, he was asking us the time in angular frequency. So since we know the frequencies, you go to 466 hers. It means the time here is equal to one or f, which is one over blind in 66 1st And this will give us 2.15 times Tend to the problem. I have a three second, and anger frequency is equal to pi, after which means it is equal to troop high attends the frequency and this will give us two pi times 466 hers. And this will give us two point 93 times. Tend to a power three radiant for a second cage. Full question be It was asking us what is the frequency and the ankle of frequency bodies Question. Okay, so the time was given us. It is 50. You second, which is 50 times tend to a power off next six second. So the frequencies is equal to one over time here it which will give us 1/50 times potential about off 96 second. And this will give us two times central power for hers. An ankle frequency is able to a troop I half with his two hands frequency. And this will give us two pi times to times 10 to the power for hers. And this will give us one point 26 times 10 to the power if I radium per second. Okay, Person C. It was asking us what? It's limits over the period and a frequency office lights. Well, the angular frequency was ranging from so for anger. Pregnancy was Reggie from 2.7 times 10 to the power 15. Brilliant per second to 4.7 times 10 to Apollo 15 radium per second. Okay, so promise information. We can get frequency, which is equal to angular frequency. Do you want to buy? So for the 1st 1 you give us to a 0.7 times central power 15 radium per second, divided by two. And this should give us I mean, Donald, check four point 30 times 10 to the power for 10 to about 14. Uh, hers have to equal to omega to you have a right to buy. And this will give us 4.7 times 10 to the power routine. Radian per second divided by two pi issue. Give us seven seven point for a ties. Gentle, about 14 Hers. Okay, so the limits off angular, let me over. Frequency will be 4.3 overtimes. Potential power 14 hers to sound going for a potential 14 hurts. Okay? And that's a living for the frequency and the living for the period. While we know the period is equal to while we're frequency. Which means that first period will be Do you want equal to one over F one, which will give us one over 4.3 old times? 10 to the 14 hers, And this will give us to a point 32 Thais. Tension about the neck. Negative. 15 hurt, uh, second. Okay. T two was just You could want over after two is equal to one over Zamboni boy times into a power 14 hers. This will give us Hey, one boy, 34 times change. About of negative. 15 second. So the then it's for the time. Here it will be 1.234 kinds. Tends about next 15 to 2.32 times into a 10 to the power of 1915 seconds. Okay, So for the last question question D, He was asking us the spirit and angular frequency. Okay. And the frequency is given as fi mega hers. So frequencies equal to fi megahertz, which is five times 10 to above six. Hers. And this will give us the periods, including one over after, which is one over frequency. We're just one over flight times potential power six hers. Any answer for the time period should be two times 10 to apo 97 seconds. An angular frequency is equal to two by half. Which is he going to? Two pi times frequency, which is five times stands above six hers. And this will give us ever see 3.14 I tend to about seven radian per second. Okay. And that's the answer. Bodies question. Thank you.

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