A source of sound is moving with a velocity of ( 50 ~ms ⁻¹ ) towards a stationary observer. The observer measures the frequency of sound as ( 500 ~Hz ). The apparent frequency of sound as heard by the observer when source is moving away from him with the same speed is (Speed of sound at room temperature ( 350 ~ms ⁻¹ ) )

Step-by-step solution

Given, velocity of source of sound ( =50 ~ms ⁻¹ ); frequency measured by observer ( =500 ~Hz ) Now, frequency of sound when source is moving towards stationary observer is [ f^ =f ( v v-v_ s ) (1) ] Frequency of sound when source is moving away from the stationary observer is [ f^ =f ( v v+v_ s ) (2) ] Using Eqs. (1) and (2), we have [ array r f^ f^ = f ( v v-v_ s ) f ( v v+v_ s ) f^ f^ = (v+v_ s ) (v-v_ s ) array ] Substitute ( v=350 ~ms ⁻¹ ; v_ s =50 ~ms ⁻ ) [ array l f^ =500 H z 500 f^ = 350+50 350-50 500 f^ = 4