8.1 Basic Concepts and Formulae
343
Sound Velocity in a Liquid
V =
γ B τ
ρ
(8.24)
where B T is the isothermal bulk modulus.
The energy in length λ is given by
E λ =
1
2
ρ 0 ω
2 A
2
λ
(8.25)
The energy density
E = E λ /λ =
1
2
ρ 0 ω
2 A
2
(8.26)
The intensity, i.e. the time rate of flow of energy per unit area of the wave front
I =
1
2
ρV A
2
ω
2
(8.27)
Intensity Level (IL):Decibel Scale
IL = 10 log(I /I 0 )
(8.28)
where log is logarithmic to base 10, I 0 is the reference intensity (the zero of the
scale) and IL is expressed in decibels.
Stationary Waves in Pipes
(i) Closed pipe (pipe closed at one end and opened at the other)
f 1 = V /4L , f 2 = 3V /4L , f 3 = 5V /4L . . .
(ii) Open pipe_(pipe opened at both ends)
f 1 = V /2L , f 2 = V /L , f 3 = 3V /2L . . .
Doppler effect is the apparent change in frequency of a wave motion when there
is relative motion between the source and the observer.
(a) Moving Source but Stationary Observer
If the source of waves of frequency f moves with velocity v and if v s is the sound
velocity in still air then the apparent frequency f would be
f
/
=
f v
v ± v s
(8.29)
where the minus sign is for approach and plus sign for separation.