The apparent frequency of a note is 200 ~Hz . When a listener is moving with a velocity of 40 ~ms ⁻¹ towards a stationary source. When he moves away from the same source with the same speed, the apparent frequency of the same note is 160 ~Hz . The velocity of sound in air (in m / s ) is

Step-by-step solution

Let f_ s be the frequency of source. The apparent frequency heard when listener moves towards source is f^ =f_ s ( v_ s +v₀ v_ s ) 200=f_ s ( v_ s +40 v_ s )...(i) The apparent frequency heard, when listener moves away from source is aligned f^ &=f_ s ( v_ s -v_ o v_ s ) 160 &=f_ s ( v_ s -40 v_ s )...(ii) aligned Dividing Eq. (i) by Eq. (ii), we get aligned & 200 160 &= v_ s +40 v_ s -40 & & 5 4 &= v_ s +40 v_ s -40 & 5 v_ s -200 &=4 v_ s +160 & v_ s &=360 ~m / s aligned