The correct options are
B Lowest frequency heard by the listener is 525 Hz
D Highest frequency heard by the listener is 555 Hz
The whistle is moving along a circular path with constant angular velocity
ω=15 rads . The linear velocity of the whistle is given by
vs=ωR where
R is radius of the circle.
At points
A and
B , the velocity of the whistle is parallel or anti-parllel to line OP; i.e., with respect to observer at
P, the whistle has maximum velocity away from
P at point
A, and minimum velocity towards
P at point
B.
Since distance
OP is large compared to radius
R , the whistle may be assumed to be moving along the line
OP . The observer, therefore, listens maximum frequency when the source is at
B moving towards the observer:
fmax=fvv−vs where
v is speed of sound in air.
Similarly, the observer listens minimum frequency when the source is at
A, moving away from the observer:
fmin=fvv+vs where
v is speed of sound in air.
For
f=540 Hz,vs=2 ft×15 rad/s=30 ft/s and
v=1100 ft/s .
we get (approx.)
fmax=555 Hz and
fmin =525 Hz