Question

A whistle of frequency 540 Hz rotates in a circle of radius 2 m at a linear speed of 30m/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 in air as 330 m/s. Can the apparent frequency be ever equal to actual ?​

Answer 1

Answer:Solution :

Apparent frequency will be minimum when the sorce is at N and moving away from the observer.

fmin=(νν+νs)f

= (330330+30)(540)=495HZ

frequency will be maximum when source is at L and approaching the observer.

fmax=(νν−νs)f=(330330−30)(540)

= 594HZ

Explanation:

Answer 2

AnSwer :-

★ Apparent frequency will be minimum when the source is at N and moving away from the observer.

$\sf n' \ _{min} = \dfrac{v}{v + v _{s}} n$

$\sf = \bigg( \dfrac{330}{330 + 30} \bigg)(540) = 495hz$

★ Apparent frequency will be maximum when source is at L and approaching the observer.

$\sf n' \ _{max} = \dfrac{v}{v - v _{s}} n$

$\sf = \bigg( \dfrac{330}{330 - 30} \bigg)(540) = 594hz$

further When the source is at M and K, angle between velocity of the source and line joint source and observer is 90° (.i.e., line of sight is perpendicular to v$\sf _s$) or

v$\sf _s$cosθ = v$\sf _s$cos90° = 0

So, there will be no Doppler effect.