Consider two sound sources S_1 and S_2 having | vedclass

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(C) According to the Doppler effect,the apparent frequency $f'$ heard by an observer is given by $f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right)$,w

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(C) According to the Doppler effect,the apparent frequency $f'$ heard by an observer is given by $f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right)$,where $f$ is the source frequency,$v$ is the speed of sound,$v_o$ is the velocity of the observer,and $v_s$ is the velocity of the source.In this problem,the source $S_1$,the observer $O$,and the source $S_2$ are all moving with the same velocity $v_s = v_o = 30\,m/s$ in the same direction.For source $S_1$: The observer is moving away from $S_1$ and $S_1$ is moving towards the observer. The apparent frequency $f_1$ is $f_1 = f \left( \frac{v - v_o}{v - v_s} \right)$. Since $v_o = v_s$,$f_1 = f \left( \frac{v - v_s}{v - v_s} \right) = f = 100\,Hz$.For source $S_2$: The observer is moving towards $S_2$ and $S_2$ is moving away from the observer. The apparent frequency $f_2$ is $f_2 = f \left( \frac{v + v_o}{v + v_s} \right)$. Since $v_o = v_s$,$f_2 = f \left( \frac{v + v_s}{v + v_s} \right) = f = 100\,Hz$.The beat frequency is the difference between the two apparent frequencies: $f_{beat} = |f_1 - f_2| = |100 - 100| = 0\,Hz$.

Consider two sound sources $S_1$ and $S_2$ having the same frequency $100\,Hz$ and the observer $O$ located between them as shown in the figure. All three are moving with the same velocity in the same direction. The beat frequency heard by the observer is .... $Hz$.

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