Question 1

Which of the following statements best describes a mechanical wave?

Accepted Answer

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

Question 2

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

Accepted Answer

The amplitude of the wave.

Question 3

Which of the following is true about electromagnetic waves?

Accepted Answer

They can travel through empty space at the speed of light.

Question 4

A wave on a string has a speed $$v$$ given by $$v = \sqrt{T/\mu}$$, where $$T is $$the tension and $$\mu is $$the linear mass density. If the tension is quadrupled, what happens to the speed of the wave?

Accepted Answer

It doubles.

Question 5

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

Accepted Answer

Transverse waves have particles moving perpendicular to the direction of wave propagation, while longitudinal waves have particles moving parallel.

Question 6

A string of length $$L is $$fixed at both ends and vibrates in its third harmonic. What is the wavelength $$\lambda of $$the standing wave?

Accepted Answer

$$\lambda = \frac{2L}{3}$$

Question 7

Two sinusoidal waves of the same amplitude and wavelength travel in the same direction along a string. If they are exactly out of phase, what is the result?

Accepted Answer

Complete destructive interference, resulting in zero amplitude.

Question 8

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

Accepted Answer

The wave number, related to the wavelength by $$k = \frac{2\pi}{\lambda}.$$

Question 9

A wave pulse travels along a string with linear mass density $$\mu = 0.01\ \mathrm{kg/m}$$ and tension $$T = 100\ \mathrm{N}. $$What is the speed of the wave?

Accepted Answer

$$v = \sqrt{\frac{100}{0.01}} = 100\ \mathrm{m/s}$$

Question 10

Which principle states that when two or more waves overlap, the resultant displacement at any point is the algebraic sum of the displacements due to each wave?

Accepted Answer

Principle of superposition.

Question 11

A standing wave on a string fixed at both ends has nodes at $$x = 0$$, $$x = L/2$$, and $$x = L. $$What harmonic is this?

Accepted Answer

Second harmonic.

Question 12

The average power transmitted by a sinusoidal wave on a string is given by $$P = \frac{1}{2} \mu \$$omega^2$$ A^2$ v. If $$the amplitude is doubled, how does the power change?

Accepted Answer

It quadruples.

Question 13

A wave described by $$y(x,t) = 0.010 \sin(10x - 50t)$$ travels along a string. What is the frequency of the wave?

Accepted Answer

$$f = \frac{50}{2\pi}\ \mathrm{Hz}$$

Question 14

Which of the following is NOT a property of mechanical waves?

Accepted Answer

They can travel through a vacuum.

Question 15

A string of length $$L is $$vibrating in its fundamental mode. What is the relationship between the length and the wavelength?

Accepted Answer

$$L = \frac{\lambda}{2}$$

Question 16

If two waves of equal amplitude and frequency travel in opposite directions along a string, what type of wave is formed?

Accepted Answer

A standing wave.

Question 17

A dot is attached to a string at an antinode of a standing wave. What is the maximum speed of the dot if the wave is $$y(x,t) = A \sin(kx) \cos(\omega t)$$?

Accepted Answer

$$v_{max} = A \omega$$

Question 18

Which of the following scenarios demonstrates resonance in a physical system?

Accepted Answer

A singer shatters a glass by singing at the glass's natural frequency.

Question 19

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

Accepted Answer

It decreases.

Question 20

Which equation correctly relates the speed $$v$$, frequency $$f$$, and wavelength $$\lambda of a $$wave?

Accepted Answer

$$v = f \lambda$$

Chapter 15: Waves I – Fundamental Concepts and Applications

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