Q: A shock wave is produced when an object moves through a medium at a speed greater than the speed of sound. What is the angle $\theta$ of the shock wave cone given by?

$\sin \theta = \frac{v_{sound}}{v_{source}}$

Question 1

Which of the following best describes the nature of sound waves in air?

Accepted Answer

Sound waves in air are longitudinal waves, with particle motion parallel to the direction of propagation.

Question 2

A sinusoidal sound wave in a fluid is described by $y(x, t) = A \cos(kx - \omega t)$. What is the corresponding expression for the sound pressure $p(x, t)$?

Accepted Answer

$p(x, t) = BkA \sin(kx - \omega t)$

Question 3

The speed of sound in a fluid is given by $v = \sqrt{\frac{B}{ho}}$. If the bulk modulus $B$ of water is $2.2 	imes 10^9$ N/m$^2$ and its density $ho$ is $1.0 	imes 10^3$ kg/m$^3$, what is the speed of sound in water?

Accepted Answer

$v = 1483$ m/s

Question 4

Which physical property of a medium primarily determines the restoring force for sound waves?

Accepted Answer

Bulk modulus $B$

Question 5

A jet engine produces a sound intensity of $10$ W/m$^2$ at a distance of $30$ m. Assuming the engine is a point source, what is the intensity at $60$ m?

Accepted Answer

$2.5$ W/m$^2$

Question 6

The sound intensity level in decibels is given by $L = 10 \log_{10} \left( \frac{I}{I_0} \right)$. If the threshold of hearing is $I_0 = 10^{-12}$ W/m$^2$ and a sound has intensity $I = 10^{-5}$ W/m$^2$, what is its intensity level?

Accepted Answer

$50$ dB

Question 7

A stopped pipe (open at one end, closed at the other) has a length $L$. What is the fundamental frequency of the pipe if the speed of sound is $v$?

Accepted Answer

$f_1 = \frac{v}{4L}$

Question 8

Two identical rifles are fired simultaneously, producing a sound intensity level of $100$ dB. What is the sound intensity level if only one rifle is fired?

Accepted Answer

$94$ dB

Question 9

A car horn emits a frequency $f_s$ as it approaches a stationary observer at speed $v_s$. What is the observed frequency $f_o$ if the speed of sound is $v$?

Accepted Answer

$f_o = f_s \frac{v}{v - v_s}$

Question 10

If the frequency of a sound drops by $10\%$ as a car passes by, what is the speed of the car? (Assume $v_{sound} = 343$ m/s)

Accepted Answer

$v = 65$ km/h

Question 11

Which of the following statements about the human ear's sensitivity to sound is correct?

Accepted Answer

The ear is most sensitive to frequencies around $1$ kHz and can detect a wide range of intensities.

Question 12

A sound wave in air has a frequency of $20$ kHz. How is this sound classified?

Accepted Answer

Ultrasound

Question 13

The intensity of a sound wave decreases with distance from a point source according to which law?

Accepted Answer

Inverse-square law: $I \propto \frac{1}{r^2}$

Question 14

A sinusoidal sound wave has displacement amplitude $A$ and wavenumber $k$. What is the amplitude of the pressure variation $p_{max}$?

Accepted Answer

$p_{max} = BkA$

Question 15

In a tube open at both ends, what is the wavelength of the fundamental mode?

Accepted Answer

$\lambda = 2L$

Question 16

The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$. What does $\gamma$ represent?

Accepted Answer

The ratio of specific heats $C_p/C_v$

Question 17

If the temperature of air increases, what happens to the speed of sound in air?

Accepted Answer

It increases

Question 18

A shock wave is produced when an object moves through a medium at a speed greater than the speed of sound. What is the angle $	heta$ of the shock wave cone given by?

Accepted Answer

$\sin 	heta = \frac{v_{sound}}{v_{source}}$

Question 19

Two pipes, each open at one end and closed at the other, have lengths $L_1 = 1.14$ m and $L_2 = 1.16$ m. If the speed of sound is $343$ m/s, what is the beat frequency when both pipes are played together in their fundamental modes?

Accepted Answer

$1.3$ Hz

Chapter 16: Sound and Hearing – Longitudinal Sound Waves, Sound Pressure, and Wave Equation

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