Two listeners are standing at different distances from
Two listeners are standing at different distances from the bed of a railway line. When a train passes them, each hears how the frequency of the train whistle changes, with the change occurring along curve 1 for one observer and along curve 2 for the other. Then,
A.
Can’t determine.
B.
Both the observers are standing at equal distance from the railway line
C.
Observer 2 is standing closer to the railway line
D.
Observer 1 is standing closer to the railway line
Please scroll down to see the correct answer and solution guide.
Right Answer is: D
SOLUTION
(fL)1=fscc−vscosθ1
(fL)2=fscc−vscosθ2
From the figure,
(fL)1>(fL)2
c−vscosθ1<c−vscosθ2
cosθ1>cosθ2
θ1<θ2
d1<d2
Thus, the curve 1 is for the listener nearer to railway line. For the listener near to moving train component of velocity toward listener vscosθ1 is almost same as the velocity of train and it varies suddenly as the velocity of train and it varies suddenly as θ approaches π2 Hence the frequency of the sound heard by the listener 1 varies suddenly. For the observer at a large distance from the railway lines the velocity component varies more gently, dropping to zero when the train is closest to the listener, therefore, the time taken for frequency change is greater.
