A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz, while the train approaches the siren. During his ret…

Question

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz, while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is

Accepted Answer

Correct answer: B. (b) Given, frequency of sound, f_s=5 kHz frequency of siren records by moving train A, f_A=5.5 kHzE frequency of siren records by moving train B, f_B=6 kHz Now, let v_s= speed of sound ∴ For observer A, frequency of siren records by trainA is given as, f_A=f_S ( v_S+v_Av_S ) or 5.5=5 ( v_S+v_Av_S ) or 1.1=1+ v_Av_S or v_A=0.1v_S … (i ) ∴ For observer B, frequency of siren records by train B is given as, f_B=f_S ( v_S+v_Bv_S )6=5 ( v_S+v_Bv_S ) or 6=5(1+ v_Bv_S) ⇒ 65=1+ v_Bv_S ⇒ 65-1= v_Bv_S ⇒ 6-55= v_Bv_S ⇒ 15= v_Bv_S ⇒ v_Bv_S=0.2 or v_B=0.2v_S…(ii) Now, from Eqs. (i) and (ii), we get or v_Bv_A= 0.2v_S0.1v_S or v_Bv_A=2 So, the ratio of the speed of train B to that of train A is v_B :v_A=2

Solution

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