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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