This document discusses the Doppler effect for sound waves emitted by a stationary source, such as a police siren, as perceived by a moving listener. It shows that the frequency perceived by the listener (f audible) can be calculated as the source frequency (f0) multiplied by 1 plus the ratio of the listener's velocity (vL) to the velocity of the sound waves (vwave). This calculation holds that the perceived frequency is higher than the actual frequency when the listener is moving towards the source and lower when moving away.

1. Doppler effect, stationary
source
f0
vwave
vListner
λ
speed=
distance
time
combined speed=
wavelength
perceived period
vL+vwave=λ f audible
Find the ratio of the
audible frequency to
the source frequency
using the two
velocities only.

2. Doppler effect, stationary
source
f0
vwave
vListner
λ
vL +vwave=λ f audible
vwave
= λ
T0
vwave=λ f 0
λ=
vwave
f 0
vL +vwave=
vwave
f 0
f audible
f audible= f 0(
(vL+vwave)
vwave
)

3. Doppler effect, stationary
source
f audible
= f 0
(
vL
+vwave
vwave
)
X=
A+B
AA simular equation.
Multiply both sides by A.
On the RHS multiply B by A/A,
which is equal to 1, so does
not affect the term.
Cancel A from every term in
the equation.
AX=A+B
AX=A+
A
A
B
X=1+
B
A
Simularly
f audible
= f 0
(1+
vL
vwave
)
Rearranges to

4. Doppler effect, stationary
source
f0
vwave
vListner
λ
QED
f audible
= f 0
(1+
vL
vwave
)

5. Doppler effect, stationary
source
Picture credit.
● http://www.clker.com/cliparts/9/5/Z/y/0/z/
man-walking-moving-hi.png