A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad / s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air =330 ms -1 )

Question

A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad / s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air =330 ms -1 ) (A) 590 Hz (B) 594 Hz (C) 598 Hz (D) 602 Hz

Tardigrade Admin · Accepted Answer

Velocity of source vs=r ω=2 × 15=30 m / s The highest frequency heard by the stationary listener f'=f((v/v-vs)) or f'=540((330/330-30))=594 Hz

Q. A whistle of frequency $540 Hz$ rotates in a horizontal circle of radius $2 m$ at an angular speed of $15 r a d / s$ . The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air $= 330 m s^{- 1}$ )

590 Hz

594 Hz

598 Hz

602 Hz

Velocity of source
$v_{s} = r ω = 2 \times 15 = 30 m / s$
The highest frequency heard by the stationary listener
$f^{'} = f (\frac{v}{v - v _{s}})$
or $f^{'} = 540 (\frac{330}{330 - 30}) = 594 Hz$

Q. A whistle of frequency 540Hz rotates in a horizontal circle of radius 2m at an angular speed of 15rad/s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air =330ms−1 )