The frequency of sound heard by an observer m | vedclass

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(D) Let $v$ be the speed of sound, $v_o$ be the speed of the observer, and $f$ be the frequency of the source.When the observer moves towards the stat

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$54$

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(D) Let $v$ be the speed of sound, $v_o$ be the speed of the observer, and $f$ be the frequency of the source.When the observer moves towards the stationary source, the observed frequency is $n_1 = f \left( \frac{v + v_o}{v} ight)$.When the observer moves away from the stationary source, the observed frequency is $n_2 = f \left( \frac{v - v_o}{v} ight)$.Given the ratio $n_1 / n_2 = 71 / 65$, we have:$\frac{v + v_o}{v - v_o} = \frac{71}{65}$.Cross-multiplying gives: $65(v + v_o) = 71(v - v_o)$.$65v + 65v_o = 71v - 71v_o$.$136v_o = 6v$.$v_o = \frac{6}{136} v = \frac{3}{68} v$.Given $v = 340 \ m/s$, we get $v_o = \frac{3}{68} 	imes 340 = 3 	imes 5 = 15 \ m/s$.To convert $m/s$ to $km/h$, multiply by $18/5$: $v_o = 15 	imes \frac{18}{5} = 3 	imes 18 = 54 \ km/h$.

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