Question 1

Which of the following best describes a mechanical wave?

Accepted Answer

A disturbance that travels through a medium, transporting energy but not matter.

Question 2

A wave on a string is created by moving the hand up and down. What type of wave is this?

Accepted Answer

Transverse wave

Question 3

A sound wave in air at 20°C has a frequency of 262 Hz. What is its wavelength? (Speed of sound $$v = 344 m/s)$$

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{344}{262} = 1.31 m$$

Question 4

For a wave, the _________ is the distance between two successive crests, while the _________ is the time elapsed between two successive crests passing by the same point.

Accepted Answer

wavelength; period

Question 5

The mathematical description of a sinusoidal wave traveling in the $$+x$$ direction is:

Accepted Answer

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

Question 6

What happens to the speed of a wave on a string if the tension in the string is increased?

Accepted Answer

The speed increases.

Question 7

A wave travels on a 50.0 cm long string with a mass of 5.00 g. The wave’s speed is 122 m/s. What is the tension force in the string? ($$v = \sqrt{\frac{F}{\mu}})$$

Accepted Answer

14.9 N

Question 8

Which equation correctly relates wave speed, wavelength, and frequency?

Accepted Answer

$$v = \lambda f$$

Question 9

What is the principle of superposition?

Accepted Answer

The total displacement is the sum of the displacements of individual waves.

Question 10

When a wave pulse reflects from a fixed end of a string, what happens?

Accepted Answer

The pulse reflects and inverts.

Question 11

When a wave pulse reflects from a free end of a string, what happens?

Accepted Answer

The pulse reflects without inverting.

Question 12

A wave function is given by $$y(x,t) = 3.7 \cos(2.2x - 5.6t). $$What is the speed of the wave?

Accepted Answer

$$v = \frac{\omega}{k} = \frac{5.6}{2.2} = 2.5 m/s$$

Question 13

Which of the following is NOT a parameter used to describe a periodic wave?

Accepted Answer

Mass of the medium

Question 14

In a longitudinal wave, what are the regions of maximum and minimum density called?

Accepted Answer

Compressions and rarefactions

Question 15

If two waves overlap and their displacements are in opposite directions, what type of interference occurs?

Accepted Answer

Destructive interference

Question 16

A string is 2 m long and has a mass of 0.04 kg. If the tension in the string is 80 N, what is the speed of a transverse wave on the string?

Accepted Answer

$$v = \sqrt{\frac{F}{\mu}} = \sqrt{\frac{80}{0.02}} = 63.25 m/s$$

Question 17

Which of the following best describes the difference between the speed of a wave and the speed of particles in the medium?

Accepted Answer

The speed of the wave is independent of the speed of the particles.

Question 18

Which formula gives the angular frequency $$\omega$$ for a wave with period $$T$$?

Accepted Answer

$$\omega = 2\pi/T$$

Question 19

A wave function is given by $$y(x,t) = A \cos(kx + \omega t). $$What direction is the wave traveling?

Accepted Answer

Negative x-direction

Question 20

If the mass per unit length of a string is doubled, what happens to the speed of a transverse wave on the string?

Accepted Answer

The speed decreases by a factor of $$\sqrt{2}.$$

Mechanical Waves: Fundamentals, Types, and Interference

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