Q: A sound wave has an intensity of $1.0 \times 10^{-8}\ \mathrm{W/m^2}$ at a distance of $2.0\ \mathrm{m}$ from the source. What is the total power emitted by the source?

$P = 5.0 \times 10^{-7}\ \mathrm{W}$

Question 1

A sound wave travels through air at $20\ ^\circ\mathrm{C}$. Using the formula $v = 331 + 0.60\ T_c$, what is the speed of sound in air at this temperature?

Accepted Answer

$v = 343\ \mathrm{m/s}$

Question 2

A sound source emits a power of $2.0\ \mathrm{W}$ uniformly in all directions. What is the intensity at a distance of $4.0\ \mathrm{m}$ from the source? Use $I = \dfrac{P}{4\pi r^2}$.

Accepted Answer

$I = 0.040\ \mathrm{W/m^2}$

Question 3

If the frequency of a sound wave is doubled while its speed remains constant, what happens to its wavelength according to $v = f\lambda$?

Accepted Answer

The wavelength is halved.

Question 4

A person hears two tuning forks producing frequencies of $256\ \mathrm{Hz}$ and $260\ \mathrm{Hz}$. What is the beat frequency?

Accepted Answer

$f_{\mathrm{beat}} = 4\ \mathrm{Hz}$

Question 5

A sound wave in water has a bulk modulus $B = 2.2 	imes 10^9\ \mathrm{N/m^2}$ and density $ho = 1000\ \mathrm{kg/m^3}$. What is the speed of sound in water?

Accepted Answer

$v = 1483\ \mathrm{m/s}$

Question 6

A jet flies at $510\ \mathrm{m/s}$ where the speed of sound is $340\ \mathrm{m/s}$. What is its Mach number?

Accepted Answer

$\mathrm{Mach} = 1.5$

Question 7

A sound has an intensity of $1.0 	imes 10^{-6}\ \mathrm{W/m^2}$. What is its sound level in decibels? Use $I_0 = 1.0 	imes 10^{-12}\ \mathrm{W/m^2}$ and $\beta = 10 \log_{10}\left(\dfrac{I}{I_0}ight)$.

Accepted Answer

$\beta = 80\ \mathrm{dB}$

Question 8

A train approaches a stationary observer at $30\ \mathrm{m/s}$. The speed of sound is $340\ \mathrm{m/s}$ and the train's whistle frequency is $500\ \mathrm{Hz}$. What frequency does the observer hear? Use $f' = f \dfrac{v + v_o}{v - v_s}$.

Accepted Answer

$f' = 545\ \mathrm{Hz}$

Question 9

For an open pipe of length $L = 0.85\ \mathrm{m}$, what is the fundamental frequency if the speed of sound is $340\ \mathrm{m/s}$? Use $f_n = \dfrac{nv}{2L}$ for $n = 1$.

Accepted Answer

$f_1 = 200\ \mathrm{Hz}$

Question 10

Two speakers emit sound waves of the same frequency and amplitude. At a certain point, the path difference is $\Delta L = 1.5\lambda$. What type of interference occurs?

Accepted Answer

Destructive interference

Question 11

A closed pipe (one end closed) is $0.5\ \mathrm{m}$ long. What is the frequency of its first overtone if the speed of sound is $340\ \mathrm{m/s}$? Use $f_n = \dfrac{nv}{4L}$ for odd $n$.

Accepted Answer

$f_3 = 510\ \mathrm{Hz}$

Question 12

A sound wave reflects from a fixed end. What happens to the phase of the wave?

Accepted Answer

The wave undergoes a phase reversal ($A \rightarrow -A$).

Question 13

If the intensity of a sound increases by a factor of 100, by how many decibels does the sound level increase?

Accepted Answer

$20\ \mathrm{dB}$

Question 14

A string transmits a wave from a light to a heavy medium. What happens to the speed of the wave? Use $v = \sqrt{\dfrac{T}{\mu}}$ for comparison.

Accepted Answer

The speed decreases.

Question 15

A supersonic jet creates a shock wave with a Mach number of $2.0$. What is the sine of the shock cone angle?

Accepted Answer

$\sin 	heta = 0.5$

Question 16

A sound wave has a frequency of $440\ \mathrm{Hz}$ and a wavelength of $0.78\ \mathrm{m}$. What is the speed of sound?

Accepted Answer

$v = 343\ \mathrm{m/s}$

Question 17

If a sound source moves away from a stationary observer, what happens to the observed frequency?

Accepted Answer

The observed frequency decreases.

Question 18

A sound wave in an ideal gas has a speed given by $v = \sqrt{\dfrac{\gamma RT}{M}}$. If the temperature doubles, what happens to the speed of sound?

Accepted Answer

The speed increases by a factor of $\sqrt{2}$.

Question 19

A sound wave has an intensity of $1.0 	imes 10^{-8}\ \mathrm{W/m^2}$ at a distance of $2.0\ \mathrm{m}$ from the source. What is the total power emitted by the source?

Accepted Answer

$P = 5.0 	imes 10^{-7}\ \mathrm{W}$

Question 20

Which of the following best describes the condition for constructive interference of two sound waves?

Accepted Answer

The path difference is an integer multiple of the wavelength: $\Delta L = n\lambda$.

Physics of Sound: Formula Summary and Key Concepts

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