Doppler Effect
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Change in frequency when a source of sound is moving
relative to an observer.
Source of sound
stationary
Hears lower
frequency
Source of sound
moving
Hears higher
frequency
Derive the expression for the apparent frequency
detected when a source of sound waves relative to
stationary observer.
Speed of source vs, source frequency fs , speed of sound v,
Source moving toward
stationary observer
Source moving away from
stationary observer
For observer
For observer
f = fs
f = fs
v
( )
v - vs
v
( )
v + vs
Source travelling towards observer
The distance the source travels in 1 period = vst =vsT = vs÷ fs
(observer) = distance travelled first wave in I period – distance
travelled by source and 2nd wave in 1 period.
= v - vs
fs
fs
fs
v
= 1 ( v – vs)
fs
For observer
f=v÷=
( )
v - vs
Derive the expression for the apparent frequency
detected when an observer moves relative to a stationary
source
Speed of observer vo, frequency fs , speed of sound v,
observer moving toward
stationary source
observer moving away
from source
For observer
For observer
f = fs
f = fs
v + vo
( )
v
v - vo
( )
v
Observer travelling towards source at speed vo
The number of waves produced in time t = ft = vt

Extra waves heard in time t = vot

Total no of waves heard = vt

+
vot

No of waves per second = frequency =
f = fs
v + vo
(
v
)
(
vt

+
v ot


÷t
As = v ÷ fs
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