Theory:

There will be no Doppler effect in the following situations, and the apparent frequency heard by the listener will be the same as the source frequency.
  • When both the source ((\S\)) and the listener ((\L\)) are at rest.
  • When ((\S\)) and ((\L\)) move in such a way that their distance from each other remains constant.
  • When the source ((\S\)) and the destination ((\L\)) are moving in opposite directions.
  • If the source is in the centre of the circle that the listener moves around in.
Numerical based on apparent change in frequency due to doppler effect:
  
Example 1:
 
A source producing a sound of frequency \(90\) \(Hz\) is approaching a stationary listener with a speed equal to (\(1/10\)) of the speed of sound. What will be the frequency heard by the listener?
  
Given:
 
Frequency(\n\)) \(=\) \(90\) \(Hz\)
 
Speed(\v\)) \(=\) (\(1/10\)) of the speed of sound
 
When the source is moving towards the stationary listener, the expression for apparent frequency is
 
n=VVVSnApplytheknownvalues,n=VV110V×90n=VV(1110)×90n=109×90n=10×10n=100Hz
 
Example 2:
 
A source producing a sound of frequency \(500\) \(Hz\) is moving towards a listener with a velocity of \(30\) \(m/s\). The speed of the sound is \(330\) \(m/s\). What will be the frequency heard by the listener?
  
Given:
 
Frequency of the sound (\(n\)) \(=\) \(500\) \(Hz\)
 
Velocity of the listener (VL) \(=\) \(30\) \(m/s\)
 
Speed of the sound(\(V\)) \(=\) \(330\) \(m/s\)
 
When the source is moving towards the stationary listener, the expression for apparent frequency is
 
n=VVVSnApplytheknownvalues,n=33033030×500n=330300×500n=110×5n=550Hz