Question 1

Which of the following statements best describes why the speed of sound is higher in steel than in air?

Accepted Answer

Steel is more elastic than air, and the speed of sound increases with elasticity.

Question 2

Given the formula for the speed of sound in air $$c = 331.4 + 0.607 	imes T$$, what is the speed of sound at $$T = 30^\circ C$$?

Accepted Answer

$$c = 349.6\ \mathrm{m/s}$$

Question 3

A guitar string has its tension increased by a factor of 4. By what factor does its natural frequency change?

Accepted Answer

It increases by a factor of 2.

Question 4

Which of the following best explains why the amplitude of vibration is maximized when the driving frequency matches the natural frequency of a system?

Accepted Answer

The system absorbs energy most efficiently at its resonant frequency.

Question 5

If the amplitude of a vibrating system drops from $$A_1 = 10$ to A_2$ = 5 in $$one cycle, what is the damping factor $$df$$?

Accepted Answer

$$df = \ln(2) = 0.693$$

Question 6

Which of the following systems is most likely to be critically damped?

Accepted Answer

A car's shock absorber

Question 7

Which of the following is true about acoustic resistance (R) and acoustic reactance (X)?

Accepted Answer

Resistance is frequency independent, while reactance is frequency dependent.

Question 8

At what frequency do the mass reactance ($$X_m) $$and compliant reactance ($$X_c) of a $$system cancel each other out?

Accepted Answer

At the system's resonant frequency ($$f_r)$$

Question 9

A tuning fork is struck and vibrates in air. Which of the following best describes the energy transformation that occurs due to acoustic resistance?

Accepted Answer

Kinetic energy is converted to thermal energy (heat).

Question 10

Which of the following statements about the speed of sound is correct?

Accepted Answer

The speed of sound is independent of the frequency of the sound wave.

Question 11

If the mass of a vibrating object is quadrupled, what happens to its natural frequency?

Accepted Answer

It decreases by a factor of 2.

Question 12

Which of the following best describes an overdamped system?

Accepted Answer

It does not oscillate and returns to equilibrium slowly.

Question 13

A sound wave travels from air into water. Which property of the medium is primarily responsible for the increase in the speed of sound?

Accepted Answer

Water's higher elasticity compared to air.

Question 14

Which of the following is true about the phase relationship between mass reactance ($$X_m) $$and compliant reactance ($$X_c$$)?

Accepted Answer

$$X_m$$ leads $$X_c by 180$$°.

Question 15

A system is described as underdamped. Which of the following best describes its behavior?

Accepted Answer

It oscillates with gradually decreasing amplitude.

Question 16

Which of the following best describes the effect of increasing the compliance of a system on its compliant reactance ($$X_c) at a $$fixed frequency?

Accepted Answer

$$X_c$$ increases.

Question 17

A medical ultrasound device uses sound waves to image the human body. Why does sound travel faster in the body than in air?

Accepted Answer

The human body is more elastic than air.

Question 18

Which of the following is a correct statement about the relationship between frequency and mass reactance ($$X_m$$)?

Accepted Answer

$$X_m$$ increases as frequency increases.

Question 19

A tuning fork is struck and produces a sound that gradually fades away. Which of the following best explains why the sound does not last forever?

Accepted Answer

Damping due to resistance and internal friction causes the amplitude to decrease over time.

Waves, Sound, Resonance, and Damping: Physics with Calculus Study Notes

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