(1) When a source is moving in a direction making an angle q w.r.t. the listener : The apparent frequency heard by listener L at rest

When source is at point A is

As source moves along AB, value of q increases, cosq decreases, goes on decreasing.

At point C,

(2) When a source of sound approaches a high wall or a hill with a constant velocity , the reflected sound propagates in a direction opposite to that of direct sound. We can assume that the source and observer are approaching each other with same velocity i.e.

(3) When a listener moves between two distant sound sources : Let be the velocity of listener away from and towards . Apparent frequency from  is

(4) When source is revolving in a circle and listener L is on one side

(6) There will be no change in frequency of sound heard, if the source is situated at the centre of the circle along which listener is moving.

 

(7) Conditions for no Doppler effect :  (i) When source (S) and listener (L) both are at rest.

(ii) When medium alone is moving.

(iii) When S and L move in such a way that distance between S and L remains constant.

(iv) When source S and listener L, are moving in mutually perpendicular directions.