Question 1

A high E string on a guitar has a linear density of $$\mu = 3.09 	imes 10$$^{-4}$$ \ \mathrm{kg/m}$$ and is under a tension of $$T = 56.40 \ \mathrm{N}. $$What is the speed of a wave on this string?

Accepted Answer

$$v = \sqrt{\frac{T}{\mu}} = 427 \ \mathrm{m/s}$$

Question 2

If the low E string on a guitar has a linear density of $$\mu = 5.78 	imes 10$$^{-3}$$ \ \mathrm{kg/m}$$, what tension is required for the wave speed to match that of the high E string ($$427 \ \mathrm{m/s}$$)?

Accepted Answer

$$T = v^2$ \mu = 1055 \ \mathrm{N}$$

Question 3

A wave on a string is described by $$y(x, t) = 0.15 \sin(2\pi x - 0.84\pi t)$$, where $$y is in $$meters, $$x in $$meters, and $$t in $$seconds. What is the amplitude of the wave?

Accepted Answer

$$0.15 \ \mathrm{m}$$

Question 4

Given the wave equation $$y(x, t) = 0.15 \sin(2\pi x - 0.84\pi t)$$, what is the wavelength?

Accepted Answer

$$\lambda = \frac{2\pi}{2\pi} = 1 \ \mathrm{m}$$

Question 5

A motorcyclist revs his engine with a sound power of $$P = 120 \ \mathrm{W} at a $$distance of $$r = 4.3 \ \mathrm{m}$$ from the observers. What is the sound intensity $$I at $$the location of the observers?

Accepted Answer

$$I = \frac{P}{4\pi r^2$} = 0.516 \ \mathrm{W/m^2$}$$

Question 6

If the sound intensity level measured by a cellphone is $$I = 2.066 \ \mathrm{W/m^2$}$$ and each motorcycle produces $$0.516 \ \mathrm{W/m^2$} at $$the same location, how many motorcycles are revving their engines?

Accepted Answer

$$n = \frac{2.066}{0.516} = 4$$

Question 7

You hear a fire truck's siren at $$460 \ \mathrm{Hz} as it $$approaches and $$410 \ \mathrm{Hz} as it $$recedes. What is the speed of the truck? (Assume speed of sound $$v = 343 \ \mathrm{m/s})$$

Accepted Answer

$$v_{truck} = \frac{f_{approach} - f_{recede}}{f_{approach} + f_{recede}} \cdot v_{sound} = 19.7 \ \mathrm{m/s}$$

Question 8

Jack is moving toward Jill at $$24.0 \ \mathrm{m/s}$$ and sounds his $$330 \ \mathrm{Hz}$$ horn. What frequency does Jill hear? (Speed of sound $$v = 343 \ \mathrm{m/s})$$

Accepted Answer

$$f' = f \frac{v + v_{observer}}{v - v_{source}} = 355 \ \mathrm{Hz}$$

Question 9

Jack hears the echo of his horn reflected from the cliff. What frequency does Jack hear in the echo? (Jack's speed $$24.0 \ \mathrm{m/s}$$, horn $$330 \ \mathrm{Hz}$$, speed of sound $$343 \ \mathrm{m/s})$$

Accepted Answer

$$f' = f \frac{v + v_{observer}}{v - v_{source}} = 380 \ \mathrm{Hz}$$

Question 10

Two loudspeakers emit $$266 \ \mathrm{Hz}$$ sound in phase and are placed at either end of a gymnasium. An observer at the center experiences constructive interference. How far must the observer walk toward either speaker to first experience destructive interference? (Speed of sound $$v = 343 \ \mathrm{m/s})$$

Accepted Answer

$$d = \frac{\lambda}{2} = 32.2 \ \mathrm{cm}$$

Question 11

Sally stands $$6.89 \ \mathrm{m} in $$front of one amplifier, which is $$7.00 \ \mathrm{m}$$ apart from the other. Both emit $$440 \ \mathrm{W} at$$ $$468 \ \mathrm{Hz} in $$phase. Is the interference at Sally's position constructive or destructive?

Accepted Answer

Constructive

Question 12

Sally walks away from the amplifier. How far from the amplifier is she when she hears loud sound for the last time? (Amplifiers $$7.00 \ \mathrm{m}$$ apart, $$f = 468 \ \mathrm{Hz}$$, $$v = 343 \ \mathrm{m/s})$$

Accepted Answer

$$d = 33.1 \ \mathrm{m}$$

Question 13

A sound wave has a frequency of $$468 \ \mathrm{Hz}$$ and travels at $$343 \ \mathrm{m/s}. $$What is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = 0.733 \ \mathrm{m}$$

Question 14

If the intensity of a sound is $$I = 0.516 \ \mathrm{W/m^2$}$$, what is the sound intensity level in decibels?

Accepted Answer

$$L = 10 \log_{10} \left( \frac{I}{I_0$} ight ) = 117 \ \mathrm{dB}$$, where $$I_0 = 1.0$$ 	imes $$10^{-12}$$ \ \mathrm{$$W/m^2$$}$$

Question 15

A wave on a string is described by $$y(x, t) = 0.15 \sin(2\pi x - 0.84\pi t). $$What is the frequency of the wave?

Accepted Answer

$$f = \frac{0.84\pi}{2\pi} = 0.042 \ \mathrm{Hz}$$

Question 16

A wave on a string is described by $$y(x, t) = 0.15 \sin(2\pi x - 0.84\pi t). $$What is the speed of the wave?

Accepted Answer

$$v = \frac{\omega}{k} = \frac{0.84\pi}{2\pi} = 0.42 \ \mathrm{m/s}$$

Physics Study Guidance: Waves, Sound, and Interference

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