Q: A sound wave travels through air with a frequency of 440 Hz and a wavelength of 0.78 m. What is the speed of sound in air based on these values?

$$v = 440 \times 0.78 = 343.2\ \mathrm{m/s}$$

Q: A standing wave is formed on a string fixed at both ends. If the string is 1.2 m long and the speed of waves on the string is 240 m/s, what is the frequency of the second harmonic?

$$f_2$$ = \dfrac{2 \times 240}{1.2} = 400\ \mathrm{Hz}$$

Q: A sound source emits a wave with a power of 2 W. If the sound spreads uniformly in all directions, what is the intensity at a distance of 4 m from the source?

$$I = \dfrac{2}{4\pi \times 4^2$} = \dfrac{2}{64\pi} \approx 0.0099\ \mathrm{W/m^2$}$$

Q: If two sound waves have frequencies of 256 Hz and 260 Hz, what is the beat frequency heard?

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

Q: A wave on a string has an amplitude of 0.05 m and a frequency of 10 Hz. If the string vibrates in SHM, what is the maximum speed of a point on the string?

$$v_{\text{max}} = 2\pi \times 0.05 \times 10 = \pi\ \mathrm{m/s} \approx 1.57\ \mathrm{m/s}$$

Question 1

A mass attached to a spring oscillates with simple harmonic motion (SHM). If the mass is doubled while keeping the spring constant the same, what happens to the period of oscillation?

Accepted Answer

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

Question 2

A sound wave travels through air with a frequency of 440 Hz and a wavelength of 0.78 m. What is the speed of sound in air based on these values?

Accepted Answer

$$v = 440 	imes 0.78 = 343.2\ \mathrm{m/s}$$

Question 3

Which of the following best describes the phenomenon of beats?

Accepted Answer

Beats occur when two waves of slightly different frequencies interfere, producing a periodic variation in amplitude.

Question 4

A closed pipe resonates at its fundamental frequency. If the length of the pipe is $$L$$, what is the wavelength of the sound produced?

Accepted Answer

$$\lambda = 4L$$

Question 5

The intensity level of a sound is measured to be 80 dB. If the intensity of the sound is doubled, what is the new intensity level in decibels?

Accepted Answer

$$83\ \mathrm{dB}$$

Question 6

Which equation correctly relates the intensity $$I of a $$wave to its power $$P$$ and the area $$A$$ over which it is distributed?

Accepted Answer

$$I = P / A$$

Question 7

A standing wave is formed on a string fixed at both ends. If the string is 1.2 m long and the speed of waves on the string is 240 m/s, what is the frequency of the second harmonic?

Accepted Answer

$$f_2$$ = \dfrac{2 	imes 240}{1.2} = 400\ \mathrm{Hz}$$

Question 8

Which of the following statements about ultrasound is correct?

Accepted Answer

Ultrasound is used in medical imaging because it can penetrate soft tissues and reflect off denser structures.

Question 9

A sound source emits a wave with a power of 2 W. If the sound spreads uniformly in all directions, what is the intensity at a distance of 4 m from the source?

Accepted Answer

$$I = \dfrac{2}{4\pi 	imes 4^2$} = \dfrac{2}{64\pi} \approx 0.0099\ \mathrm{W/m^2$}$$

Question 10

Which of the following best explains why standing waves form in a pipe closed at one end?

Accepted Answer

The closed end acts as a node and the open end acts as an antinode, allowing only certain wavelengths to resonate.

Question 11

If two sound waves have frequencies of 256 Hz and 260 Hz, what is the beat frequency heard?

Accepted Answer

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

Question 12

Which of the following is true about the relationship between sound intensity and loudness?

Accepted Answer

Loudness is related to intensity logarithmically.

Question 13

A wave on a string has an amplitude of 0.05 m and a frequency of 10 Hz. If the string vibrates in SHM, what is the maximum speed of a point on the string?

Accepted Answer

$$v_{	ext{max}} = 2\pi 	imes 0.05 	imes 10 = \pi\ \mathrm{m/s} \approx 1.57\ \mathrm{m/s}$$

Question 14

Which of the following is a correct application of the principle of superposition?

Accepted Answer

When two waves overlap, the resulting displacement at any point is the sum of the individual displacements.

Question 15

A person hears a sound at 60 dB. If the intensity of the sound is $$I_0$$, what is the formula for the intensity level in decibels?

Accepted Answer

$$L = 10 \log_{10} \left( \dfrac{I}{I_0$} \right)$$

Question 16

Which of the following is an example of infrasound?

Accepted Answer

Sound waves with frequencies below 20 Hz produced by earthquakes.

Question 17

A hospital uses ultrasound to image a fetus. If the speed of sound in tissue is 1540 m/s and the frequency of the ultrasound is 3 MHz, what is the wavelength of the ultrasound?

Accepted Answer

$$\lambda = \dfrac{1540}{3 	imes 10^6$} \approx 0.000513\ \mathrm{m}$$

Question 18

A guitar string vibrates at its fundamental frequency. If the length of the string is halved, what happens to the fundamental frequency?

Accepted Answer

The fundamental frequency doubles.

Question 19

Which of the following best describes the energy transfer in a traveling wave?

Accepted Answer

Energy is transferred from one point to another without the transfer of matter.

Waves & Acoustics: Principles and Applications

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