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

Answer:

(a) lowest frequency=577 Hz

(b) highest frequency=608 Hz

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

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

For (b) highest frequency

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