A source of sound of frequency v is moving towards a wall with speed u. Find the number of beats heard by a stationary observer on the ground when:
(i) observer is between source and wall.
(ii) source is between observer and wall.

(i) When observer is between source and wall, then source is approaching both observer and wall. 

 
The apparent frequency of wave received by observer is, 
                       
The apparent frequency of wave incident on wall is,
                        
As the wall is stationary, therefore the frequency of wave reflected is same as that of wave incident in it.
Thus, the frequency of wave reflected by the wall is v₂.
Now the observer receives a wave of frequency v₁ from source and a wave of v₂ after reflection from the wall.
Therefore the number of beats heard per second is, 
                        
(ii) When the source is between observer and wall, then source is moving away from the observer and approaching towards the wall. 
 
The apparent frequency of wave received by observer is,
                       
The apparent frequency of wave incident on wall is,
                       
Therefore number of beats heard per second is,