Question

A whistle of frequency 540 H_(Z) rotates in a circle of radius 2 mat a linear speed of 30 m//s . What is the lowest and highest frequency heard by an observer a long distance away at rest with respect to the centre of circle ? Take speed of sound of sound in air as 330 m//s. Can the apparent frequency be ever equal to actual ?

Answer 1

Given:

A whistle of frequency, F =  540 Hz.

It rotates in a circle of radius, r = 2m.

Linear speed Vw  = 30m/s

Speed of sound in air as 330m/s

To Find:

The lowest and highest frequency heard by an observer a long distance away at rest with respect to the center of circle.

Solution:

Apparent frequency will be minimum when the whistle is at D, where it is moving away from the observer.

• Fmin = $\frac{V}{V + Vw} F$
• Fmin =  540  x 330/(330 + 30 ) = 495 Hz

Apparent frequency will be maximum when the whistle is at B, where it is moving towards from the observer.

• Fmax = $\frac{V}{V - Vw}$F
• Fmax = 540 x 330/330 - 30 = 594 Hz

• Vw in the direction of sound = 0, when the object is at A and C .

• Then apparent frequency will be equal to actual frequency.

The  lowest frequency heard by the observer is 495Hz and the highest frequency heard by the observer is 594Hz.

Apparent frequency will be equal to actual if the whistle is at rest with respect to the direction along the observer.