Q: A student hears an echo 2.0 seconds after shouting toward a distant wall. If the speed of sound in air is 340 m/s, how far away is the wall?

$$d = \frac{340\ \mathrm{m/s} \times 2.0\ \mathrm{s}}{2} = 340\ \mathrm{m}$$

Q: A pipe open at both ends has a length of 1.5 m. What is the wavelength of the fundamental frequency?

$$\lambda = 2L = 2 \times 1.5\ \mathrm{m} = 3.0\ \mathrm{m}$$

Q: A sound wave resonates in a tube of length 1.0 m with one end closed. What is the wavelength of the lowest resonating frequency?

$$\lambda = 4L = 4 \times 1.0\ \mathrm{m} = 4.0\ \mathrm{m}$$

Q: Two speakers separated by 1.0 m emit sound waves of wavelength 0.5 m. If a listener is 10 m away, what is the distance from the central maximum to the first maximum?

$$x = \frac{\lambda L}{d} = \frac{0.5 \times 10}{1.0} = 5.0\ \mathrm{m}$$

Q: A tuning fork produces a frequency of 256 Hz. Another fork produces 260 Hz. What is the beat frequency?

$$f_{\text{beat}} = |260 - 256| = 4\ \mathrm{Hz}$$

Q: A flute (open tube) and a clarinet (closed tube) are both 0.85 m long. What is the ratio of their fundamental wavelengths?

Open tube: $$\lambda_{\text{open}} = 2L = 1.7\ \mathrm{m}$$; Closed tube: $$\lambda_{\text{closed}} = 4L = 3.4\ \mathrm{m}$$; Ratio $$= \frac{1.7}{3.4} = 0.5$$

Question 1

A sound wave has a frequency of 500 Hz and travels through air at 340 m/s. What is its wavelength?

Accepted Answer

$$\lambda = \frac{340\ \mathrm{m/s}}{500\ \mathrm{Hz}} = 0.68\ \mathrm{m}$$

Question 2

A student hears an echo 2.0 seconds after shouting toward a distant wall. If the speed of sound in air is 340 m/s, how far away is the wall?

Accepted Answer

$$d = \frac{340\ \mathrm{m/s} 	imes 2.0\ \mathrm{s}}{2} = 340\ \mathrm{m}$$

Question 3

Which of the following best explains why the intensity of sound is measured in decibels (dB)?

Accepted Answer

The human ear detects sounds in a very large range of intensities.

Question 4

A pipe open at both ends has a length of 1.5 m. What is the wavelength of the fundamental frequency?

Accepted Answer

$$\lambda = 2L = 2 	imes 1.5\ \mathrm{m} = 3.0\ \mathrm{m}$$

Question 5

A sound wave resonates in a tube of length 1.0 m with one end closed. What is the wavelength of the lowest resonating frequency?

Accepted Answer

$$\lambda = 4L = 4 	imes 1.0\ \mathrm{m} = 4.0\ \mathrm{m}$$

Question 6

Two speakers separated by 1.0 m emit sound waves of wavelength 0.5 m. If a listener is 10 m away, what is the distance from the central maximum to the first maximum?

Accepted Answer

$$x = \frac{\lambda L}{d} = \frac{0.5 	imes 10}{1.0} = 5.0\ \mathrm{m}$$

Question 7

A tuning fork produces a frequency of 256 Hz. Another fork produces 260 Hz. What is the beat frequency?

Accepted Answer

$$f_{	ext{beat}} = |260 - 256| = 4\ \mathrm{Hz}$$

Question 8

A sound source moves toward a stationary observer. What happens to the frequency and wavelength of the sound as heard by the observer?

Accepted Answer

The observer hears a higher frequency and a shorter wavelength.

Question 9

A jet plane flies faster than the speed of sound. What phenomenon is observed and why?

Accepted Answer

A shock wave (sonic boom) is produced because the plane moves faster than the sound waves it generates.

Question 10

A flute (open tube) and a clarinet (closed tube) are both 0.85 m long. What is the ratio of their fundamental wavelengths?

Accepted Answer

Open tube: $$\lambda_{	ext{open}} = 2L = 1.7\ \mathrm{m}$$; Closed tube: $$\lambda_{	ext{closed}} = 4L = 3.4\ \mathrm{m}$$; Ratio $$= \frac{1.7}{3.4} = 0.5$$

Question 11

A sound wave travels from a guitar string into the air. Which property remains unchanged?

Accepted Answer

Frequency

Question 12

If the distance from a sound source is doubled, by what factor does the intensity decrease?

Accepted Answer

The intensity decreases by a factor of $$\frac{1}{4}.$$

Question 13

A closed tube has a length of 0.6 m. What is the frequency of the third harmonic if the speed of sound is 340 m/s?

Accepted Answer

$$f_3$$ = \frac{3v}{4L} = \frac{3 	imes 340}{4 	imes 0.6} = 425\ \mathrm{Hz}$$

Question 14

Two sound waves arrive at a listener and differ in path length by $$\lambda/2. $$What type of interference occurs?

Accepted Answer

Destructive interference

Question 15

A sound wave in water (speed = 1400 m/s) has a frequency of 700 Hz. What is its wavelength?

Accepted Answer

$$\lambda = \frac{1400\ \mathrm{m/s}}{700\ \mathrm{Hz}} = 2.0\ \mathrm{m}$$

Question 16

A person hears thunder 9 seconds after seeing lightning. How far away did the lightning strike? (Assume speed of sound is 340 m/s.)

Accepted Answer

$$d = 340\ \mathrm{m/s} 	imes 9\ \mathrm{s} = 3060\ \mathrm{m}$$

Question 17

Which of the following materials will sound travel fastest through, based on the table provided?

Accepted Answer

Aluminum

Question 18

A pipe open at both ends has a fundamental frequency of 200 Hz. What is the frequency of the third harmonic?

Accepted Answer

$$f_3 = 3$$ 	imes 200\ \mathrm{Hz} = 600\ \mathrm{Hz}$$

Sound Waves: Properties, Sources, Interference, and Applications

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