A whistle of frequency 660 Hz moves in a circle of radius 1 m at an angular speed of 10 rad/s. The highest frequecny heard by a listener at a long distance and at rest with respect to the center of the circle is (Let speed of sound =340 m//s.)

Options

A. 700 Hz
B. 640 Hz
C. 720 Hz
D. 680 Hz

Answer

D

Explanation

Given, frequency whistle `f_(0)=660Hz` speed of sound =340m/s
angular speed of whistle, `omega=10` rad/s and radius of circle, r=1 m.
Since, we know that the maximum frequency heard by listener, if whistle has tangential velocity towards the listener as shown in figure,

linear velocity, `v=omegar`
`=10xx1=10m//s`
As, given that, there is long distance between whistle and listener i.e., `theta~~0`.
Now, the apparent frequency,
`f=(f_(0)v)/(v-v_(s))`
`f=(660xx340)/(340-10)=680Hz`
Hence, the correct option is