Question 1

A sound wave travels through air with a frequency of $$500 \ \mathrm{Hz}$$ and a wavelength of $$0.68 \ \mathrm{m}. $$What is the speed of the sound wave?

Accepted Answer

$$v = 340 \ \mathrm{m/s}$$

Question 2

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

Accepted Answer

In a transverse wave, particle displacement is perpendicular to wave propagation; in a longitudinal wave, it is parallel.

Question 3

A water wave has an amplitude of $$0.2 \ \mathrm{m}$$ and a wavelength of $$1.5 \ \mathrm{m}. If $$the frequency is $$2 \ \mathrm{Hz}$$, what is the equation for the wave if it moves in the positive $$x-$$direction?

Accepted Answer

$$y = 0.2 \sin\left(\dfrac{2\pi}{1.5}x - 4\pi t\right)$$

Question 4

If the period of a wave is $$0.25 \ \mathrm{s}$$, what is its frequency?

Accepted Answer

$$f = 4 \ \mathrm{Hz}$$

Question 5

A wave is described by $$y = 3.0 \cos(6.0x - 2.0t). $$What is the wavelength of the wave?

Accepted Answer

$$\lambda = \dfrac{2\pi}{6.0} = 1.05 \ \mathrm{m}$$

Question 6

Which of the following statements about the propagation of sound waves in air is correct?

Accepted Answer

The air molecules oscillate back and forth, but the phase of the wave and its energy move forward.

Question 7

Given the wave equation $$y = 2.0 \cos(5.0x - 2.5t)$$, what is the angular frequency $$\omega$$?

Accepted Answer

$$\omega = 2.5 \ \mathrm{rad/s}$$

Question 8

A wave has a wave number $$k = 4 \ \mathrm{rad/m}$$ and an angular frequency $$\omega = 8 \ \mathrm{rad/s}. $$What is the speed of the wave?

Accepted Answer

$$v = \dfrac{\omega}{k} = 2 \ \mathrm{m/s}$$

Question 9

If a wave is described by $$y = A \sin(kx - \omega t)$$, what does the sign of $$\omega t$$ indicate?

Accepted Answer

The direction of wave propagation

Question 10

A student observes a water wave and measures the time for 10 crests to pass a fixed point as $$5 \ \mathrm{s}. $$What is the frequency of the wave?

Accepted Answer

$$f = 2 \ \mathrm{Hz}$$

Question 11

Which of the following best describes the phase $$	heta in $$the wave equation $$y = A \sin(kx - \omega t)$$?

Accepted Answer

It represents the position within a cycle at a given $$x$$ and $$t.$$

Question 12

A wave on a string is described by $$y = 0.5 \sin(4x - 6t). $$What is the period $$T of $$the wave?

Accepted Answer

$$T = \dfrac{2\pi}{6} = 1.05 \ \mathrm{s}$$

Question 13

A sound wave has a frequency of $$440 \ \mathrm{Hz}$$ and travels at $$330 \ \mathrm{m/s}. $$What is its wavelength?

Accepted Answer

$$\lambda = \dfrac{v}{f} = 0.75 \ \mathrm{m}$$

Question 14

If the phase of a wave at $$x = 2 \ \mathrm{m}$$ and $$t = 4 \ \mathrm{s} is$$ $$	heta = 0$$ for the wave $$y = 2.0 \cos(5.0x - 2.5t)$$, what is the value of $$y at $$this point?

Accepted Answer

$$y = 2.0$$

Question 15

Which of the following is a correct expression for the wave number $$k in $$terms of wavelength $$\lambda$$?

Accepted Answer

$$k = \dfrac{2\pi}{\lambda}$$

Question 16

A wave is described by $$y = 1.5 \sin(3x - 6t). $$What is the frequency $$f of $$the wave?

Accepted Answer

$$f = \dfrac{6}{2\pi} = 0.955 \ \mathrm{Hz}$$

Question 17

Which of the following real-world examples best illustrates a longitudinal wave?

Accepted Answer

Sound traveling through air from a speaker to your ear

Question 18

If a wave equation is $$y = A \sin(kx + \omega t)$$, in which direction is the wave traveling?

Accepted Answer

Negative $$x-$$direction

Question 19

A wave has a wavelength of $$2 \ \mathrm{m}$$ and a period of $$0.5 \ \mathrm{s}. $$What is its speed?

Accepted Answer

$$v = \dfrac{\lambda}{T} = 4 \ \mathrm{m/s}$$

Question 20

Which of the following is NOT a property of a harmonic wave described by $$y = A \sin(kx - \omega t)$$?

Accepted Answer

The amplitude depends on $$x$$ and $$t$$

Wave Equation and Basic Wave Properties

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