A highway truck has two horns A and B. When s | vedclass

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Question

(A) Let the frequencies of horns $A$ and $B$ be $n_A$ and $n_B$, respectively.Given that the driver records $50$ beats in $10$ seconds when both horns

Vedclass · Accepted Answer

$75$

Vedclass · Answer

(A) Let the frequencies of horns $A$ and $B$ be $n_A$ and $n_B$, respectively.Given that the driver records $50$ beats in $10$ seconds when both horns are sounded together:$|n_A - n_B| = \frac{50}{10} = 5 \,Hz$.When the truck moves towards a wall with speed $v_s = 10 \,m/s$, the frequency of the echo heard by the driver is given by the Doppler effect formula:$n_B' = n_B \left( \frac{v + v_s}{v - v_s} \right)$, where $v = 330 \,m/s$ is the speed of sound.$n_B' = n_B \left( \frac{330 + 10}{330 - 10} \right) = n_B \left( \frac{340}{320} \right) = n_B \left( \frac{17}{16} \right) = 1.0625 n_B$.The beat frequency with the echo is $n_B' - n_B = 5 \,Hz$.$1.0625 n_B - n_B = 5 \implies 0.0625 n_B = 5$.$n_B = \frac{5}{0.0625} = 80 \,Hz$.Given that decreasing $n_A$ increases the beat frequency $|n_A - n_B|$, it implies $n_A Since $|n_A - n_B| = 5$, we have $n_B - n_A = 5$.$n_A = n_B - 5 = 80 - 5 = 75 \,Hz$.

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