Page 200 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 15] WAVES AND SOUND 185

Attenuation refers to a loss of power, so the power gain of this type of cable is −23 dB per 100 m. Since the
cable length here is 20 m, the power gain is (20/100)(−23 dB) =−4.6 dB. From the solution to Prob. 15.11,
G dB −4.6
P out = P in antilog = (25 W) antilog
10 10
= (25 W)(0.35) = 8.7W

Less than half the power reaches the antenna.

SOLVED PROBLEM 15.13
An audio system is made up of components with the following power gains: preamplifier, +35 dB;
attenuator, −10 dB; amplifier, +70 dB. What is the overall gain of the system?
Since power gains in decibels are logarithmic quantities, the overall gain in decibels of a system of several
devices is equal to the sum of the separate gains in decibels of the devices:

G (overall) = G 1 + G 2 + G 3 + ···
G (overall) =+35 dB − 10 dB + 70 dB =+95 dB

DOPPLER EFFECT
When there is relative motion between a source of waves and an observer, the apparent frequency of the waves
is different from their frequency f S at the source. This change in frequency is called the Doppler effect. When
the source approaches the observer, as in Fig. 15-6 (a), the wavelength of the waves is shorter than when there is
no relative motion, and the observed frequency is higher. When the source moves away from the observer, as in
(b), the wavelength of the waves is longer and the observed frequency is lower. Similar effects occur when the
source is stationary and the observer is moving toward or away from it.

(a) (b)
Fig. 15-6
In the case of sound waves, the frequency f that a listener hears is given by

v + v L
f = f S sound
v − v S
In this formula v is the velocity of sound, v L is the velocity of the listener (considered positive for motion toward
the source and negative for motion away from the source), and v s is the velocity of the source (considered positive
for motion toward the listener and negative for motion away from the listener).
The Doppler effect in electromagnetic waves (light and radio waves are examples) obeys the formula

1/2
1 + (v/c)
f = f S electromagnetic waves
1 − (v/c)