Question 1

Which of the following statements correctly distinguishes mechanical waves from electromagnetic waves?

Accepted Answer

Mechanical waves require a physical medium to propagate, while electromagnetic waves do not require a medium.

Question 2

A transverse wave is traveling along a string. Which direction do the particles of the string move relative to the direction of wave propagation?

Accepted Answer

Perpendicular to the direction of propagation

Question 3

A sinusoidal wave on a string is described by the wave function $$y(x, t) = A \sin(kx - \omega t). $$What does the parameter $$A$$ represent?

Accepted Answer

The amplitude, which is the maximum displacement from equilibrium

Question 4

The speed of a wave on a string under tension $$T$$ and with mass per unit length $$\mu is $$given by which equation?

Accepted Answer

$$v = \sqrt{\frac{T}{\mu}}$$

Question 5

A sound wave travels through air at $$20^\circC. $$Using the formula $$v = (331\,	ext{m/s}) \left[1 + \frac{T_c}{273}ight]$$, what is the speed of sound in air at this temperature?

Accepted Answer

$$v = 343\,	ext{m/s}$$

Question 6

Which of the following best describes the relationship between frequency $$f$$ and period $$T of a $$wave?

Accepted Answer

$$f = \frac{1}{T}$$

Question 7

A string is vibrating with a frequency $$f$$ and amplitude $$A. $$The power transmitted by the wave is proportional to which of the following?

Accepted Answer

The square of the frequency and the square of the amplitude

Question 8

A pulse is traveling to the right along a string with speed $$v. If $$its initial shape is $$f(x) at$$ $$t=0$$, what is its shape at time $$t$$?

Accepted Answer

$$f(x - vt)$$

Question 9

Which of the following is true about the speed of sound in different media?

Accepted Answer

Sound travels fastest in solids, slower in liquids, and slowest in gases.

Question 10

A sound wave in a solid rod has speed $$v = \sqrt{\frac{Y}{\rho}}$$, where $$Y is $$Young's modulus and $$\rho is $$density. If the density doubles and Young's modulus remains constant, what happens to the speed of sound?

Accepted Answer

It decreases by a factor of $$\sqrt{2}$$

Question 11

A periodic sound wave in a tube is generated by an oscillating piston. The distance between two successive compressions is:

Accepted Answer

The wavelength $$\lambda$$

Question 12

The pressure variation in a sound wave is given by $$\Delta P = \Delta P_{max} \sin(kx - \omega t). $$What is $$\Delta P_{max} in $$terms of density $$\rho$$, wave speed $$v$$, and displacement amplitude $$s_{max}$$?

Accepted Answer

$$\Delta P_{max} = \rho v \omega s_{max}$$

Question 13

Which of the following is NOT a requirement for the propagation of a mechanical wave?

Accepted Answer

A vacuum

Question 14

A wave on a string has a wavelength $$\lambda$$ and period $$T. $$What is the speed $$v of $$the wave?

Accepted Answer

$$v = \frac{\lambda}{T}$$

Question 15

A lightning bolt is seen and thunder is heard 5 seconds later. Using the speed of sound in air as $$343\,	ext{m/s}$$, how far away did the lightning strike?

Accepted Answer

$$1715\,	ext{m}$$

Question 16

Which of the following best describes a longitudinal wave?

Accepted Answer

The particles of the medium move parallel to the direction of wave propagation.

Question 17

If the frequency of a sound wave is increased while the speed of sound remains constant, what happens to the wavelength?

Accepted Answer

It decreases

Question 18

Which of the following is a correct expression for the angular frequency $$\omega in $$terms of frequency $$f$$?

Accepted Answer

$$\omega = 2\pi f$$

Question 19

A sinusoidal wave is described by $$y(x, t) = A \sin(kx - \omega t + \phi). $$What does the parameter $$\phi$$ represent?

Accepted Answer

The phase constant

Question 20

Which of the following statements about ideal waves is correct?

Accepted Answer

Ideal waves have a single frequency and are infinitely long.

Waves on a String and Sound Waves: Fundamental Concepts and Mathematical Descriptions

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