Q: A dolphin uses echolocation to detect an object $$75\ \mathrm{m}$$ away. If the speed of sound in water is $$1500\ \mathrm{m/s}$$, how long after emitting the pulse does the dolphin receive the echo?

$$t = \dfrac{2d}{v} = \dfrac{2 \times 75}{1500} = 0.1\ \mathrm{s}$$

Question 1

Which of the following best describes a mechanical wave?

Accepted Answer

A wave that propagates as oscillations of matter, transferring energy through a medium.

Question 2

What is the main difference between transverse and longitudinal waves?

Accepted Answer

In transverse waves, oscillations are perpendicular to the direction of wave propagation, while in longitudinal waves, oscillations are parallel to the direction of propagation.

Question 3

A sound wave travels through water with a frequency of $$100,000\ \mathrm{Hz}. If $$the speed of sound in water is $$1500\ \mathrm{m/s}$$, what is the wavelength of the sound wave?

Accepted Answer

$$\lambda = \dfrac{v}{f} = \dfrac{1500}{100,000} = 0.015\ \mathrm{m}$$

Question 4

Which statement about the speed of sound in different media is correct?

Accepted Answer

Sound travels faster in solids than in liquids or gases because the density and molecular interactions are greater.

Question 5

A string of length $$L is $$fixed at both ends. What is the wavelength of the fundamental frequency (first harmonic) of the standing wave formed on the string?

Accepted Answer

$$\$$lambda_1$$ = 2L$$

Question 6

If the amplitude of a sinusoidal wave is doubled, how does the energy transported by the wave change?

Accepted Answer

The energy increases by a factor of 4, since $$E \propto A^2$.

Question 7

A dolphin uses echolocation to detect an object $$75\ \mathrm{m}$$ away. If the speed of sound in water is $$1500\ \mathrm{m/s}$$, how long after emitting the pulse does the dolphin receive the echo?

Accepted Answer

$$t = \dfrac{2d}{v} = \dfrac{2 	imes 75}{1500} = 0.1\ \mathrm{s}$$

Question 8

Which of the following best describes constructive interference?

Accepted Answer

When two waves overlap and their amplitudes add, resulting in a larger amplitude.

Question 9

A string is vibrating in its third harmonic. If the length of the string is $$L$$, what is the wavelength of the standing wave?

Accepted Answer

$$\$$lambda_3$$ = \dfrac{2L}{3}$$

Question 10

The equation $$y(x, t) = A \sin(kx - \omega t)$$ describes a wave. What does $$A$$ represent?

Accepted Answer

The amplitude of the wave, which is the maximum displacement from equilibrium.

Question 11

When a wave encounters a boundary and is reflected, under what condition does the reflected wave pick up a phase shift of $$180^{\circ}$$?

Accepted Answer

When the wave reflects from a boundary where the medium is more dense.

Question 12

The intensity $$I of a $$wave is defined as the power transported per unit area. If the power transported by a wave is $$P$$ and the area is $$A$$, which equation correctly expresses intensity?

Accepted Answer

$$I = \dfrac{P}{A}$$

Question 13

A string of length $$1.5\ \mathrm{m} is $$fixed at both ends and vibrates at its second harmonic. What is the wavelength of the standing wave?

Accepted Answer

$$\$$lambda_2$$ = L = 1.5\ \mathrm{m}$$

Question 14

Which of the following is true about standing waves on a string fixed at both ends?

Accepted Answer

Nodes are points of zero displacement and must occur at both ends of the string.

Question 15

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

Accepted Answer

The speed doubles, since $$v \propto \sqrt{T}.$$

Question 16

Which of the following is a correct statement about the period $$T$$ and frequency $$f of a $$wave?

Accepted Answer

$$T = \dfrac{1}{f}$$

Question 17

A wave pulse travels down a rope and reaches a fixed end. What happens to the pulse upon reflection?

Accepted Answer

The pulse is inverted upon reflection.

Question 18

If two waves of equal amplitude and frequency travel in opposite directions on a string, what phenomenon can occur?

Accepted Answer

A standing wave can be formed due to interference.

Question 19

Which property of a wave determines how 'bright' light appears or how 'loud' sound is perceived?

Accepted Answer

Intensity, which is proportional to the square of the amplitude.

Wave Motion: Principles and Types

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