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
Diffcult
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(b) Observer is moving away from siren $ 1$ and towards the siren $2.$
Hearing frequency of sound emitted by siren $1$
${n_1} = n\left( {\frac{{v - {v_0}}}{v}} \right) = 330\,\left( {\frac{{330 - 2}}{{330}}} \right) = 328Hz$
Hearing frequency of sound emitted by siren $2$
${n_2} = n\,\left( {\frac{{v + {v_0}}}{v}} \right) = 330\,\left( {\frac{{330 + 2}}{{330}}} \right) = 332Hz$
Hence, beat frequency $ = {n_2} - {n_1} = 332 - 328 = 4.$
Hearing frequency of sound emitted by siren $1$
${n_1} = n\left( {\frac{{v - {v_0}}}{v}} \right) = 330\,\left( {\frac{{330 - 2}}{{330}}} \right) = 328Hz$
Hearing frequency of sound emitted by siren $2$
${n_2} = n\,\left( {\frac{{v + {v_0}}}{v}} \right) = 330\,\left( {\frac{{330 + 2}}{{330}}} \right) = 332Hz$
Hence, beat frequency $ = {n_2} - {n_1} = 332 - 328 = 4.$
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