Q. Two sirens situated one kilometer apart are producing sound of frequency $330\ Hz.$ An observer starts moving from one siren to the other with a speed of $2\ m/s.$ If the speed of sound be $330\ m/s,$ what will be the beat frequency heard by the observer
A) 8
B) 4
C) 6
D) 1
Explanation
(b) Observer is moving away from siren 1 and towards the siren 2.
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Hearing frequency of sound emitted by siren 1
$n_{1} = n\left( \frac{v - v_{O}}{v} \right) = 330\left( \frac{330 - 2}{330} \right) = 328Hz$
Hearing frequency of sound emitted by siren 2
$n_{2} = n\left( \frac{v + v_{O}}{v} \right) = 330\left( \frac{330 + 2}{330} \right) = 332Hz$
Hence, beat frequency $= n_{2} - n_{1} = 332 - 328 = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.