dP mom:
dt
¼ ΔF ¼ ρ 0 Ac 0 ΔV
and the pressure perturbation, Δp ¼ ΔF/A, becomes,
Δp ¼ ρ 0 c 0 ΔV,
which is in agreement with Eq. (1.87) above.
By using Eq. (1.87) the sound intensity can also be written as
I ¼
1
2
Δp
ð Þ
2
ρ 0 c 0
:
ð1:88Þ
1.9.1 Typical Sound Intensity in Normal Conversation
The typical sound energy in a normal conversation is about 10μW. A person listening
about 1 m away will receive an intensity given by
I ¼
10μW
4π 1
ð Þ
2
¼ 0:8μWm
À2 ,
so that the excess pressure Δp is given by
Δp ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
2ρ 0 c 0 I
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 Â 1:25 Â 340 Â 0:8 Â 10
À6
p
¼ 0:026Nm
À2 ,
which is a tiny fraction of the atmospheric pressure. The velocity amplitude ΔV m is
about 0.006 cm/s and the typical molecular displacement amplitude is approximately
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Fig. 1.5 Piston motion generating a small compression wave that moves to the right-hand side at
the speed of sound (see text)
40
1 Brief Outline of the Equations of Fluid Flow