Page 197 - Schaum's Outline of Theory and Problems of Applied Physics

182 WAVES AND SOUND [CHAP. 15

Logarithms are not limited to powers of 10 that are whole numbers. For instance,
5 = 10 0.669 therefore log 5 = 0.669
240 = 10 2.380 therefore log 240 = 2.380

n
Logarithms are defined only for positive numbers. The quantity 10 is positive whether n is negative, positive,
n
or 0; and since n is the logarithm of 10 , it can only describe a positive number.
The antilogarithm of a quantity n is the number N whose logarithm it is. That is,
If log N = n then antilog n = N

x
To find an antilogarithm with a calculator, enter the value of the logarithm and press the 10 (INV LOG on some
calculators) button. For instance,
If log 5 = 0.669 then antilog 0.669 = 5
Because of the way logarithms are defined, the logarithm of a product equals the sum of the logarithms of
the factors:

log xy = log x + log y
Other useful relations are
x
log = log x − log y
y
n
log x = n log x

SOUND
Sound waves are longitudinal waves that consist of varying pressures. They can travel through solids, liquids,
and gases. As a sound wave passes a point, the medium becomes alternately squeezed and expanded, so the wave
consists of regions of compression and rarefaction that follow each other. Figure 15-5 shows how such regions
move outward from the vibrating cone of a loudspeaker. The changes in pressure cause our eardrums to vibrate
with the same fequency, and this produces the sensation of sound.

Rarefaction
(low pressure)

Compression
(high pressure)
Fig. 15-5. From Konrad B. Krauskopf and Arthur Beiser, The Physical Universe, 10th Ed., c 2003, The McGraw-Hill
Companies. Reproduced with permission of The McGraw-Hill Companies.
The speed of sound is a constant for a given material under given conditions; in air at 1-atm pressure and
20 C it is 343 m/s. Sound travels faster in solids and liquids than in gases.
◦
When sound waves spread out uniformly in space, their intensity decreases inversely with the square of the
distance R from their source. Thus if the intensity of a certain sound is I 1 at the distance R 1 , its intensity I 2 at