At the beach, you time wave crests hitting the shore and determine there are 20 seconds between crests. Determine the frequency of the wave. Would you expect this frequency to change if you made your measurements further out from the shore?

A speaker produces a tone at a frequency of $660 \mathrm{~Hz}$. The speaker cone has a maximum displacement of $0.3 \mathrm{~cm}$ when turned on. Assume the speed of sound in air is $343 \mathrm{~m} / \mathrm{s}$. Construct mathematical and graphical representations of the resulting wave.

A speaker produces a tone at a frequency of $500 \mathrm{~Hz}$. The speaker cone has a maximum displacement of $0.7 \mathrm{~cm}$ when turned on. Assume the speed of sound in air is $343 \mathrm{~m} / \mathrm{s}$. Construct mathematical and graphical representations of the resulting wave.

Now try going the other way! Given the two graphs shown, determine the wave properties and write distance and time mathematical representations for the wave. What is the speed of this wave?

A coach shouts "Go!" from the finish line of a 100.0-m track to the runners. It takes $292 \mathrm{~ms}$ for the 171-Hz sound wave to reach them. Calculate the speed of sound in air and the wavelength of her voice.

You are using sonar over a spot in the ocean known to be $91.8 \mathrm{~m}$ deep. The system emits a $50.0-\mathrm{kHz}$ pulse into the water. It takes $120.0 \mathrm{~ms}$ for the sound to travel to the ocean floor and back to the sonar system. Determine the speed of sound in the ocean and the wavelength of the sonar pulse.

What causes a change in wave speed? What causes a change in frequency? Can you change the frequency of a wave to cause a change in the speed? How can you affect the wavelength of a wave?

The distance between the peaks of water waves seems to depend on how close they are to the shore, as shown in the image. Qualitatively describe the pattern that you observe.

A car horn vibrates at a frequency of $250 \mathrm{Hz}$. Determine the frequency a stationary observer hears as the car (a) approaches at a speed of $20 \mathrm{m} / \mathrm{s}$ and (b) departs at $20 \mathrm{m} / \mathrm{s}$.If the car is stationary, what frequency is heard (c) by an observer approaching the car at $20 \mathrm{m} / \mathrm{s}$ and (d) by an observer departing from the car at $20 \mathrm{m} / \mathrm{s}$?

Using the data in the earlier exercise.

$$\begin{array}{cr} \hline \textbf{Number of Hours} & \textbf{Frequency}\\ \hline 1.0–3.9 & 25\hspace{20pt}\\ 4.0–6.9 & 34\hspace{20pt}\\ 7.0–9.9 & 48\hspace{20pt}\\ 10.0–12.9 & 29\hspace{20pt}\\ 13.0–15.9 & 23\hspace{20pt}\\ 16.0–18.9 & 17\hspace{20pt}\\ 19.0–21.9 & 13\hspace{20pt}\\ 22.0–24.9 & 7\hspace{20pt}\\ 25.0–27.9 & 3\hspace{20pt}\\ 28.0–30.9 & 1\hspace{20pt}\\ \hline \end{array}$$

$\textbf{a.}\hspace{10pt}$ Compute the cumulative frequencies for the classes in the frequency distribution.

$\textbf{b.}\hspace{10pt}$ Construct a frequency ogive for the frequency distribution.

$\textbf{c.}\hspace{10pt}$ Compute the cumulative relative frequencies for the classes in the frequency distribution.

$\textbf{d.}\hspace{10pt}$ Construct a relative frequency ogive, using the same classes.

A series $R-L-C$ ac circuit with a sinusoidal voltage source of angular frequency $\omega$ has a total reactance $X$. If this frequency is doubled, the reactance becomes
A. $4 X$.
B. $2 X$.
C. $X / 2$.
D. $X / 4$.
E. none of the above.

A 20-kilogram mass is attached to a spring. If the frequency of simple harmonic motion is $2/\pi$ cycles/s, what is the spring constant $k$? What is the frequency of simple harmonic motion if the original mass is replaced with an 80-kilogram mass?

Consider a sound wave of frequency $f$ generated in air by a loudspeaker. When this sound wave reaches a nearby lake, the sound wave propagates into the water, where it has the same frequency $f$. What is the ratio of the wavelength of the wave in the water to the wavelength in air?

Radar-based speed detection works by sending an electromagnetic wave out from a source and examining the Doppler shift of the reflected wave. Suppose a wave of frequency $10.6 \mathrm{GHz}$ is sent toward a car moving away at a speed of $32.0 \mathrm{~km} / \mathrm{h}$. What is the difference between the frequency of the wave emitted by the source and the frequency of the wave an observer in the car would detect?