Q: A sound wave travels through air with a velocity of $$v = 346\ \text{m/s}. If $$the frequency of the sound is $$f = 440\ \text{Hz}$$, what is its wavelength?

$$\lambda = \frac{v}{f} = \frac{346}{440} = 0.786\ \text{m}$$

Q: A string vibrates with a frequency of $$f = 50\ \text{Hz}$$ and a wavelength of $$\lambda = 2\ \text{m}. $$What is the velocity of the wave?

$$v = f \lambda = 50 \times 2 = 100\ \text{m/s}$$

Q: If two waves with amplitudes $$A_1 = 2$$\ \text{cm}$$ and A_2$ = 3\ \text{cm}$$ meet in phase, what is the resultant amplitude according to the principle of superposition?

$$A = A_1$ + A_2$ = 5\ \text{cm}$$

Q: A pipe open at both ends has a length $$L = 1.5\ \text{m}. $$What is the wavelength of the fundamental (first harmonic)?

$$\lambda = 2L = 3.0\ \text{m}$$

Q: A sound wave has a period of $$T = 0.002\ \text{s}. $$What is its frequency?

$$f = \frac{1}{T} = \frac{1}{0.002} = 500\ \text{Hz}$$

Question 1

Which of the following best describes the difference between transverse and longitudinal waves?

Accepted Answer

Transverse waves have oscillations perpendicular to the direction of energy transfer, while longitudinal waves have oscillations parallel to it.

Question 2

A sound wave travels through air with a velocity of $$v = 346\ 	ext{m/s}. If $$the frequency of the sound is $$f = 440\ 	ext{Hz}$$, what is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{346}{440} = 0.786\ 	ext{m}$$

Question 3

Which of the following is an example of a longitudinal wave?

Accepted Answer

Sound waves

Question 4

In a graphical representation of a transverse wave, what does the amplitude correspond to?

Accepted Answer

The maximum displacement from the equilibrium position

Question 5

A string vibrates with a frequency of $$f = 50\ 	ext{Hz}$$ and a wavelength of $$\lambda = 2\ 	ext{m}. $$What is the velocity of the wave?

Accepted Answer

$$v = f \lambda = 50 	imes 2 = 100\ 	ext{m/s}$$

Question 6

Which phenomenon explains why you can hear sound around a corner, even though you cannot see around it?

Accepted Answer

Diffraction

Question 7

A student observes two waves of equal amplitude and frequency traveling in opposite directions along a string. What is the result of their superposition?

Accepted Answer

A standing wave with nodes and antinodes

Question 8

If two waves with amplitudes $$A_1 = 2$$\ 	ext{cm}$$ and A_2$ = 3\ 	ext{cm}$$ meet in phase, what is the resultant amplitude according to the principle of superposition?

Accepted Answer

$$A = A_1$ + A_2$ = 5\ 	ext{cm}$$

Question 9

A pipe open at both ends has a length $$L = 1.5\ 	ext{m}. $$What is the wavelength of the fundamental (first harmonic)?

Accepted Answer

$$\lambda = 2L = 3.0\ 	ext{m}$$

Question 10

Which statement best describes resonance in a mechanical system?

Accepted Answer

Resonance occurs when a system absorbs energy most efficiently at its natural frequency.

Question 11

A sound wave has a period of $$T = 0.002\ 	ext{s}. $$What is its frequency?

Accepted Answer

$$f = \frac{1}{T} = \frac{1}{0.002} = 500\ 	ext{Hz}$$

Question 12

Which of the following best explains constructive interference?

Accepted Answer

Two waves meet and their amplitudes add, resulting in a larger amplitude.

Question 13

A pipe closed at one end has a length $$L = 0.8\ 	ext{m}. $$What is the wavelength of the fundamental (first harmonic)?

Accepted Answer

$$\lambda = 4L = 3.2\ 	ext{m}$$

Question 14

Which property of a wave determines how much energy it carries?

Accepted Answer

Amplitude

Question 15

A seismic S-wave travels through the Earth with a frequency of $$f = 10\ 	ext{Hz}$$ and a velocity of $$v = 5000\ 	ext{m/s}. $$What is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{5000}{10} = 500\ 	ext{m}$$

Question 16

Which of the following is NOT a property of mechanical waves?

Accepted Answer

They can travel through a vacuum.

Question 17

A string fixed at both ends forms a standing wave with three antinodes. What harmonic is this?

Accepted Answer

Third harmonic

Question 18

Which scenario best illustrates the efficient transfer of energy in a resonating system?

Accepted Answer

A singer shatters a glass by singing at its natural frequency.

Question 19

Which of the following best describes rarefaction in a longitudinal wave?

Accepted Answer

The region where particles are furthest apart

Question 20

A string of length $$L = 1.2\ 	ext{m} is $$fixed at both ends. What is the frequency of the second harmonic if the wave velocity is $$v = 240\ 	ext{m/s}$$?

Accepted Answer

$$f_2$$ = \frac{2v}{L} = \frac{2 	imes 240}{1.2} = 400\ 	ext{Hz}$$

Waves: Properties, Types, and Sound Phenomena

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