37.2 Sound Wave Characteristics

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The characteristics of a sound wave are described by a pressure oscillation of a pure tone. A “pure tone” is

a sinusoidal pressure wave of a specific frequency and amplitude, propagating at a velocity determined by

the temperature and pressure of the medium (air).

Let us consider a hypothetical sound field in a duct with constant cross-sectional area, as shown in

Figure 37.1a. A reciprocating piston at the left end emits the sound wave and it propagates toward the

right-side end along the indicated axis. It is detected by a microphone at the right end. Figure 37.1b

shows the instantaneous pressure distribution in a duct at time t ¼ t0: Figure 37.1c shows the pressure

variation of the time history detected by the microphone at x ¼ x0:

37-1

© 2005 by Taylor & Francis Group, LLC

The wavelength, l; is the distance between

successive two peaks in the waveform in Figure

37.1b. Wavelength is related to the frequency, f ;

and the velocity of wave propagation, c; by

l ¼

c

f ðft or mÞ ð37:1Þ

The period, T; of the sinusoidal wave is the time

interval required for one complete cycle, as

depicted in Figure 37.1b. The period, T; is related

to the frequency, f ; by

T ¼

1

f ðsecÞ ð37:2Þ

37.2.1 Velocity of Sound

The velocity of sound is identical to the velocity of

wave propagation, c; and in air it is given by

c ¼

ffiffiffiffiffiffi

gp0

r

s

ðft=sec or m=secÞ ð37:3Þ

where g denotes the ratio of specific heat, p0

denotes the ambient or equilibrium pressure,

and r denotes the ambient or equilibrium density.

For air, g is taken as 1.4. Equation 37.3 then

becomes

c ¼

ffiffiffiffiffiffiffiffi

1:4p0

r

s

ðft=sec or m=secÞ ð37:4Þ

which can be further simplified by the fact that the ratio p0=r is related to the temperature of the gas.

On assuming that the air behaves virtually as an ideal gas, the velocity, c; is related to the absolute

temperature in degrees Kelvin (K) by

c ¼ 20:05

ffiffi

T p ðm=secÞ ð37:5Þ

where T; the temperature in degrees Kelvin, is

T ¼ 273:28 þ ð8CÞ K ð37:6Þ

Example 37.1

Calculate the velocity of sound, c; giving the temperature of 158C.

Solution

T ¼ 273:28 þ 158 ¼ 288:2 K; then

c ¼ 20:05

ffiffiffiffiffiffiffi

288:2 p ¼ 340:4 m=sec

is obtained. This value means a typical velocity of sound in the air.

FIGURE 37.1 (a) Propagating sound wave in a duct;

(b) instantaneous pressure distribution; (c) pressure

variation in time history detected by a microphone

at x ¼ x0:

37-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

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