Source and observer, both start moving simultaneously from origin, one along X-axis and the other along Y-axis with speed of source equal to twice the speed of observer. The graph between the apparent frequency ($n$’) observed by observer and time $t$ in figure would be

Question

Dr. Abubacker · Accepted Answer

(b) Let speed of observer be $v_{L} = v$ along $Y$-axis and speed of source the $v_{s} = 2v_{L} = 2v$ along $X$-axis
$	herefore PS = 2(OL)$
[image:15_image87.emf]
$\cos{\alpha = \frac{2}{\sqrt{5}}and\ \cos{\beta =}}\frac{2}{\sqrt{5}}$
Now , apparent frequency $n^{''}$ is given by
$n^{''} = \frac{(v - v_{L}\cos\beta)n}{(v + v_{L}\cos\alpha)}$
Where v is velocity of sound.
$n^{''} = \frac{(v - v\sqrt{5})n}{(v + 4v\sqrt{5})}$
Clearly, $n^{''}$ is constant, but $n^{''} < n$. This is shown in curve (b).

Q. Source and observer, both start moving simultaneously from origin, one along X-axis and the other along Y-axis with speed of source equal to twice the speed of observer. The graph between the apparent frequency ($n$’) observed by observer and time $t$ in figure would be

Explanation

Reviewed by Dr. Abubacker

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