Question 1

Which of the following statements best describes the difference between transverse and longitudinal waves?

Accepted Answer

In transverse waves, the medium is displaced perpendicular to the direction of wave propagation, while in longitudinal waves, it is displaced parallel.

Question 2

A string is under tension $$F$$ and has a mass per unit length $$\mu. $$What is the speed $$v of a $$transverse wave traveling along the string?

Accepted Answer

$$v = \sqrt{F/\mu}$$

Question 3

A periodic wave has a wavelength $$\lambda$$ and frequency $$f. $$What is the correct formula for its speed $$v$$?

Accepted Answer

$$v = \lambda f$$

Question 4

A boat is moored in a fixed location. If the spacing between wave crests is $$20\ \mathrm{m}$$ and the speed of the waves is $$5\ \mathrm{m/s}$$, how long does it take the boat to go from the top of a crest to the bottom of a trough?

Accepted Answer

$$4\ \mathrm{sec}$$

Question 5

Which of the following is true about mechanical waves?

Accepted Answer

Mechanical waves transport energy, but not matter.

Question 6

A wave pulse traveling on a string reflects from a fixed end. What happens to the pulse upon reflection?

Accepted Answer

It is reflected and inverted.

Question 7

Two sinusoidal waves of equal amplitude and frequency travel in opposite directions on a string. What is the result of their superposition?

Accepted Answer

A standing wave with nodes and antinodes.

Question 8

For a string fixed at both ends of length $$L$$, what are the possible wavelengths $$\lambda_n$$ for standing waves?

Accepted Answer

$$\lambda_n = 2L/n$$

Question 9

A guitar string is tightened, increasing its tension $$F. $$What effect does this have on the fundamental frequency $$f_1 of $$the string?

Accepted Answer

The fundamental frequency increases.

Question 10

The mathematical description of a sinusoidal wave moving in the $$+x$$ direction is $$y(x, t) = A \cos(kx - \omega t). $$What is the value of the wave number $$k$$?

Accepted Answer

$$k = 2\pi/\lambda$$

Question 11

A wave on a string has amplitude $$A$$, angular frequency $$\omega$$, and mass per unit length $$\mu. $$What is the average power $$P_{avg}$$ carried by the wave?

Accepted Answer

$$P_{avg} = \frac{1}{2} \mu \$$omega^2$$ A^2$ v$$

Question 12

If the amplitude of a wave on a string is doubled, by what factor does the average power carried by the wave change?

Accepted Answer

It increases by a factor of 4.

Question 13

Which of the following best describes the principle of superposition?

Accepted Answer

The total displacement at any point is the sum of the displacements of individual waves.

Question 14

A standing wave on a string has nodes and antinodes. What is true at a node?

Accepted Answer

The displacement is zero.

Question 15

A pressure wave in a fluid is an example of which type of mechanical wave?

Accepted Answer

Longitudinal wave

Question 16

A wave pulse traveling on a string encounters a boundary with a heavier string. What happens to the pulse?

Accepted Answer

Part of the pulse is reflected (not inverted), and part is transmitted.

Question 17

For a string fixed at both ends, what is the frequency $$f_n of $$the $$nth $$harmonic?

Accepted Answer

$$f_n = n v / 2L$$

Question 18

Which of the following is a real-world example of a mechanical wave that does NOT transport matter?

Accepted Answer

The 'wave' performed by spectators in a stadium.

Question 19

A string is fixed at one end and passes over a pulley to a hanging mass. If the mass is increased, what happens to the speed of waves on the string?

Accepted Answer

The speed increases.

Question 20

A surface wave on water is best described as:

Accepted Answer

A combination of transverse and longitudinal waves.

Mechanical Waves: Principles, Types, and Properties

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