When the observer moves towards the stationary source with velocity V 1 , the apparent frequency of the emitted note is F 1 . When the observer moves away from the source with velocity V 1 , the apparent frequency is F 2 . If V is the velocity of sound in air and F 1 F 2 = 2 t h e n V V 1 = ?

Step-by-step solution

F 1 F 2 = 2 , Speed of approach = Speed of leaving The apparent frequency of sound observed by observer when it is approaching source is given by F 1 = V + V 1 V . f 0 ....(i) When observer is moving away from source F 2 = V − V 1 V f 0 ....... (ii) Here f 0 is the frequency of sound wave Taking ratio of (i) with (ii) we have F 1 F 2 = V V - V 1 × V + V 1 V = V + V 1 V - V 1 ∴ 2 = V + V 1 V - V 1 ∴ 2 V - 2 V 1 = V + V 1 ∴ 2 V - V = 3 V 1 ∴ V V 1 = 3