Page 195 - Schaum's Outline of Theory and Problems of Applied Physics

180 WAVES AND SOUND [CHAP. 15

The wavelength λ (Greek letter lambda) of a periodic wave is the distance between adjacent wave crests
[Fig. 15-4(b)]. Frequency and wavelength are related to wave velocity by

v = f λ
Wave velocity = (frequency)(wavelength)
The amplitude A of a wave is the maximum displacement of the particles of the medium through which the
wave passes on either side of their equilibrium positions. In a transverse wave, the amplitude is half the distance
between the top of a crest and the bottom of a trough (Fig. 15-4).
The intensity I of a wave is the rate at which it transports energy per unit area perpendicular to its direc-
tion of motion. The intensity of a mechanical wave (one that involves moving matter, in contrast to, say, an
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electromagnetic wave) is proportional to f , the square of its frequency, and to A , the square of its amplitude.
SOLVED PROBLEM 15.1
As a phonograph record turns, a certain groove passes the needle at 25 cm/s. If the wiggles in the groove
are 0.1 mm apart, what is the frequency of the sound that results?

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Here the wavelength of the wiggles is λ = 0.1mm = 10 , so they pass the needle at the rate of
v 0.25 m/s
f = = = 2500 Hz
λ 10 −4 m
This is therefore the frequency of the sound waves produced by the electronic system of the record player.

SOLVED PROBLEM 15.2
The velocity of sound in seawater is 1531 m/s. Find the wavelength in seawater of a sound wave whose
frequency is 256 Hz.

v 1531 m/s
λ = = = 5.98 m
f 256 Hz

SOLVED PROBLEM 15.3
A tuning fork vibrating at 300 Hz is placed in a tank of water. (a) Find the frequency and wavelength of
the sound waves in the water. (b) Find the frequency and wavelength of the sound waves produced in the
air above the tank by the vibrations of the water surface. The velocity of sound is 4913 ft/s in water and
1125 ft/s in air.

(a) In the water, the frequency of the sound waves is the 300 Hz of their source, and their wavelength is
4913 ft/s
v 1
λ 1 = = = 16.4ft
f 300 Hz
(b) In the air, the frequency of the sound waves is the same as the frequency of their source, which is the vibrating
water surface. Hence f = 300 Hz. The wavelength is different, however:
v 2 1125 ft/s
λ 2 = = = 3.75 ft
f 300 Hz
SOLVED PROBLEM 15.4

A certain radar emits 9400-MHz radio waves in groups 0.08 µs in duration. (The time needed for these
groups to reach a target, be reflected, and return to the radar indicates the distance of the target.) The
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velocity of these waves, like other electromagnetic waves, is c = 3.00×10 m/s. Find (a) the wavelength
of these waves, (b) the length of each wave group, which governs how precisely the radar can measure
distances, and (c) the number of waves in each group.