Question 1

Which of the following statements best describes the central feature of wave motion?

Accepted Answer

Energy is transferred over a distance, but matter is not.

Question 2

A mechanical wave requires which of the following to propagate?

Accepted Answer

A physical medium and a source of disturbance.

Question 3

In a transverse wave, how do the particles of the medium move relative to the direction of wave propagation?

Accepted Answer

Perpendicular to the direction of wave propagation.

Question 4

Consider a 'Mexican wave' in a stadium, where people stand and raise their arms as the pulse arrives and then sit down again. Is this an example of a transverse or longitudinal wave?

Accepted Answer

Transverse wave, because the motion is perpendicular to the direction of the wave.

Question 5

The general form for a sinusoidal traveling wave on a string is given by $$y(x, t) = A \sin(kx - \omega t). $$What does the parameter $$A$$ represent?

Accepted Answer

The amplitude, or maximum displacement from equilibrium.

Question 6

Given the wave function $$y(x, t) = 0.20 \sin(0.50x - 2.0t)$$, where $$x$$ and $$y$$ are in meters and $$t in $$seconds, what is the velocity of the wave?

Accepted Answer

$$v = 4.0\ \mathrm{m/s}$$

Question 7

Which of the following best describes the difference between the motion of the wave and the motion of the medium in a traveling wave?

Accepted Answer

The wave propagates through the medium, but the medium's particles oscillate about their equilibrium positions.

Question 8

A wave on a string is described by $$y(x, t) = 0.10 \sin(2x - 5t)$$, where $$x$$ and $$y$$ are in meters and $$t in $$seconds. What is the wavelength of the wave?

Accepted Answer

$$\lambda = \frac{2\pi}{2} = \pi\ \mathrm{m}$$

Question 9

Which of the following is NOT a type of mechanical wave?

Accepted Answer

Radio wave

Question 10

A microwave oven produces waves described by $$\cos(50.1t - 1.1x)$$, where $$t is in $$seconds and $$x in $$meters. What is the frequency of the wave?

Accepted Answer

$$f = \frac{50.1}{2\pi}\ \mathrm{Hz}$$

Question 11

If the equation of a transverse wave on a string is $$y(x, t) = 0.20 \sin(0.50x - 2.0t)$$, what is the amplitude, frequency, wavelength, and velocity of the wave?

Accepted Answer

Amplitude: $$0.20\ \mathrm{m}$$, Frequency: $$0.32\ \mathrm{Hz}$$, Wavelength: $$12.6\ \mathrm{m}$$, Velocity: $$4.0\ \mathrm{m/s}$$

Question 12

Which equation correctly describes the motion of an element on a string for a sinusoidal wave traveling to the right?

Accepted Answer

$$y(x, t) = A \sin(kx - \omega t)$$

Question 13

A pulse travels to the right along a string. If the shape and position of the pulse at $$t = 0 is$$ $$y(x, 0)$$, what is the shape of the pulse at time $$t$$?

Accepted Answer

$$y(x, t) = y(x - vt, 0)$$

Question 14

Rank the following waves according to their (a) wave speed and (b) maximum speed of an element of the medium perpendicular to the direction of travel of the wave (transverse speed):
(1) $$y_1(x$$, t) = 2 \sin(2x - 3t)$$
(2) y_2$(x, t) = 3 \sin(3x - 2t)
(3$$) $$y_3(x$$, t) = 1 \sin(x - t)$$

Accepted Answer

(a) $$v_3$$ \u003e $$v_1$$ \u003e $$v_2$$; (b) $$v_{max,2} \u003e v_{max,1} \u003e v_{max,3}$$

Question 15

Which of the following best describes a longitudinal wave?

Accepted Answer

Particles of the medium move parallel to the direction of wave propagation.

Question 16

The frequency $$f of a $$sinusoidal wave is related to its angular frequency $$\omega by $$which equation?

Accepted Answer

$$f = \frac{\omega}{2\pi}$$

Question 17

A sinusoidal wave is set up in a string. If the wave moves to the right, what is the correct sign convention in the wave function?

Accepted Answer

The wave function is $$y(x, t) = A \sin(kx - \omega t).$$

Question 18

Which of the following is a correct statement about the propagation of a disturbance in a mechanical wave?

Accepted Answer

The disturbance requires a physical medium and a source of energy.

Question 19

For a sinusoidal wave described by $$y(x, t) = A \sin(kx - \omega t)$$, what is the transverse acceleration of an element on the string?

Accepted Answer

$$a = -A \$$omega^2$$ \sin(kx - \omega t)$$

Chapter 16 – Wave Motion: Propagation, Types, and Sinusoidal Waves on Strings

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