The three wave pulses in FIGURE Q16.1 travel along the same stretched string. Rank in order, from largest to smallest, their wave speeds $v_{\text{A}}$, $v_{\text{B}}$, and $v_{\text{C}}$. Explain.

FIGURE Q16.1

A wave pulse travels along a stretched string at a speed of $200\text{cm}\text{/}\text{s}$. What will be the speed if:

1. The string’s tension is doubled?

2. The string’s mass is quadrupled (but its length is unchanged)?

3. The string’s length is quadrupled (but its mass is unchanged)?

Note: Each part is independent and refers to changes made to the original string.

FIGURE Q16.3 is a history graph showing the displacement as a function of time at one point on a string. Did the displacement at this point reach its maximum of 2 mm before or after the interval of time when the displacement was a constant 1 mm?

FIGURE Q16.3

FIGURE Q16.4 shows a snapshot graph and a history graph for a wave pulse on a stretched string. They describe the same wave from two perspectives.

1. In which direction is the wave traveling? Explain.

2. What is the speed of this wave?

FIGURE Q16.4

Rank in order, from largest to smallest, the wavelengths ${\text{λ}}_{\text{a}}$, ${\text{λ}}_{\text{b}}$, and ${\text{λ}}_{\text{c}}$ for sound waves having frequencies  $f_{\text{a}}=100\text{Hz,}$ $f_{\text{b}}=1000\text{Hz,}$ and $f_{\text{c}}=10\text{,}000\text{Hz}$. Explain.

A sound wave with wavelength ${\text{λ}}_0$ and frequency $f_0$ moves into a new medium in which the speed of sound is $v_1=2v_0$. What are the new wavelength ${\text{λ}}_1$ and frequency $f_1?$ Explain.

What are the amplitude, wavelength, frequency, and phase constant of the traveling wave in FIGURE Q16.7?

FIGURE Q16.7

FIGURE Q16.8 is a snapshot graph of a sinusoidal wave at $t=1.0\text{s}$. What is the phase constant of this wave?

FIGURE Q16.8

FIGURE Q16.9 shows the wave fronts of a circular wave. What is the phase difference between (a) points 1 and 2, (b) points 3 and 4, and (c) points 5 and 6?

FIGURE Q16.9

Sound wave A delivers 2 J of energy in 2 s. Sound wave B delivers 10 J of energy in 5 s. Sound wave C delivers 2 mJ of energy in 1 ms. Rank in order, from largest to smallest, the sound powers $P_{\text{A}}$, $P_{\text{B}}$, and $P_{\text{C}}$ of these three sound waves. Explain.

One physics professor talking produces a sound intensity level of 52 dB. It’s a frightening idea, but what would be the sound intensity level of 100 physics professors talking simultaneously?

You are standing at $x=0\text{m,}$ listening to a sound that is emitted at frequency $f_0$. The graph of FIGURE Q16.12 shows the frequency you hear during a 4-second interval. Which of the following describes the sound source? Explain your choice.

1. It moves from left to right and passes you at $t=2\text{s}$.

2. It moves from right to left and passes you at $t=2\text{s}$.

3. It moves toward you but doesn’t reach you. It then reverses direction at $t=2\text{s}$.

4. It moves away from you until $t=2\text{s}$. It then reverses direction and moves toward you but doesn’t reach you.

FIGURE Q16.12