A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with

Question

A whistle emitting a sound of frequency 440 Hz is tied to a string of 1.5 m length and rotated with an angular velocity of $20 \mathrm{rad} \mathrm{s}^{-1}$ in the horizontal plane. Calculate the maximum frequency heard by an observer stationed at a large distance from the whistle. Report the nearest integer in Hz\

Professor PC Thomas Classes · Answer

The observer is stationed at a large distance from the whistle. The whistle, which is the source of sound, is rotated in a circle. $v_{S}=$ Speed of source\ or $\quad v_{S}=R \omega$ or $v_{S}=(1.5)(20)$\ or $\quad v_{S}=30 \mathrm{~m} / \mathrm{s}$\ The observer receives maximum frequency in position $A$ of whistle. Minimum frequency is received in position $B$ of the whistle.\ $	herefore f_{	ext {max }}=f\left(\frac{v}{v-v_{S}}ight)$\ or $f_{\max }=440\left(\frac{330}{330-30}ight) \mathrm{Hz}$\ or $f_{\max }=\frac{440 	imes 330}{300}$ or $f_{\max }=484 \mathrm{~Hz}$\ Again, $f_{\min }=f\left(\frac{v}{v+v_{S}}ight)$\ or $f_{	ext {min }}=440\left(\frac{330}{330+30}ight)$\ or $f_{\min }=\frac{440 	imes 330}{360}$\ or $f_{\min }=403.3 \mathrm{~Hz}$.\ $	herefore \quad$ Range of frequencies heard $=403.3 \mathrm{~Hz}$ to 484 Hz\