Question

A whistle of frequency 592 Hz moves in a circle of radius 64.7 cm at an angular speed of 13.8 rad/s. What are (a) the lowest and (b) the highest frequencies heard by a listener a long distance away, at rest with respect to the center of the circle?

Answer 1

(a) lowest frequency=577 Hz

(b) highest frequency=608 Hz

Step-by-step explanation:

Given data

f(whistle frequency)=592 Hz

ω(angular speed)=13.8 rad/s

r(radius)=64.7 cm=0.647 m

To find

(a) Lowest frequency

(b) highest frequency

Solution

From Doppler effect

f=f×{(v±vd)/(v±vs)}

Where

v is speed of sound

Vd is speed detector relative to the medium(vd=0)

Vs is the speed of the source

Since

v=rω

For (a) lowest frequency

`f^(i)=f((v)/(v+rw) )\\f^(i)=(592Hz)((343m/s)/(343m/s+(0.647m)(13.8rad/s)) )\\f^(i)=577Hz`

For (b) highest frequency

`f^(i)=f((v)/(v-rw) )\\f^(i)=(592Hz)((343m/s)/(343m/s-(0.647m)(13.8rad/s)) )\\f^(i)=608Hz`