Solutions to problems on waves

S17 Click here to read the question.

Since the wave crests pass the boat once every 3.0 seconds, we know that the frequency of the water waves is f = 1 / 3.0 seconds = 0.33 Hz. The distance between wave crests (at a fixed time) is the wavelength. The fisherman's observation says that the wavelength is 7.5 m. Then we know that
wavespeed = wavelength x frequency
or, the wavespeed = (7.5 m) x (0.33 Hz) = 2.5 m/s
Note, the fisherman could observe different wavelength water waves as well. Those waves would also travel with a speed of 2.5 m/s, since the wave speed is a property of the medium. Longer wavelength water waves would have smaller frequencies and shorter wavelength water waves would have higher frequencies to keep the wavespeed constant at 2.5 m/s.

S18 Click here to read the question

The sound wave produced by striking the middle C key on a piano has a frequency of 440 Hz. From the relation
wavespeed = wavelength x frequency,
we can solve for the wavelength of the sound wave, since we know the wavespeed is the speed of sound in air (344 m/s).
wavelength = wavespeed / frequency,
or, wavelength = 344 m/s / 440 Hz = 0.78 m
Note, the sound wave produced from striking the C key one octave higher than middle C has a frequency of 880 Hz. This sound wave has exactly the same wave speed (344 m/s). It's wavelength is half as large (0.39 m) as the sound wave produced by striking the middle C key. Sound waves an octave lower in frequency (220 Hz) would have twice the wavelength (1.56 m).

Rossing 3.1 To solve this problem we have to realize that all waves have their wave properties (frequency and wavelength) related to the wavespeed via

wavespeed = wavelength x frequency

Electromagnetic waves always travel through space at a wave speed of 3 x 10⁸ m/s (this is 186,000 miles per second!). So the frequency of the different waves can be determined from

frequency = wavespeed / wavelength

This means...

for radio waves with wavelength = 100 m, the frequency is 3 MHz
for red light waves with wavelength = 750 nm, the frequency is 4 x 10¹⁴ Hz
for violet light waves with wavelength = 500 nm, the frequency is 6 x 10¹⁴ Hz
for radar waves with wavelength = 3 cm, the frequency is 1 x 10¹⁰ Hz = 10 GHz.

Rossing 3.4 To solve this problem we have to realize that all waves have their wave properties (frequency and wavelength) related to the wavespeed via

wavespeed = wavelength x frequency

Sound waves travel through air with a wavespeed of 344 m/s, so we can find the frequency via

frequency = wavespeed / wavelength

This means...

when the wavelength equals the diameter of a 15 inch woofer, the sound wavelength is 0.38 m and the frequency is 902 Hz
when the wavelength equals the diameter of a 3 inch tweeter, the sound wavelength is 0.076 m and the frequency is 4510 Hz.

Rossing 3.6 The low frequency end of the audible spectrum of sounds is at a frequency of 50 Hz, meaning sound waves of length = 6.9 m. The high frequency end of the audible spectrum of sounds is at a frequency of 15,000 Hz, meaning sound waves of length 2.3 cm.

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Last updated: 14 Oct 1998Comments: bland@indiana.edu