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(C) Let the speed of car $B$ be $v_B$. Both cars $A$ and $B$ are moving towards the stationary siren.$1$. Frequency heard by car $B$ from the stationa

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(C) Let the speed of car $B$ be $v_B$. Both cars $A$ and $B$ are moving towards the stationary siren.$1$. Frequency heard by car $B$ from the stationary siren $(n_1)$:Since the source is stationary and the observer (car $B$) is moving towards it,the frequency is given by:$n_1 = n_s \left( \frac{v + v_B}{v} \right) = 170 \left( \frac{340 + v_B}{340} \right) = \frac{1}{2} (340 + v_B)$$2$. Frequency heard by car $B$ from car $A$ $(n_2)$:Car $A$ is the source moving towards the observer (car $B$),and car $B$ is the observer moving away from the source (car $A$).$n_2 = n_A \left( \frac{v - v_B}{v - v_A} \right) = 180 \left( \frac{340 - v_B}{340 - 20} \right) = 180 \left( \frac{340 - v_B}{320} \right) = \frac{18}{32} (340 - v_B) = \frac{9}{16} (340 - v_B)$$3$. Condition for no beats:For no beats,the frequencies must be equal: $n_1 = n_2$$\frac{1}{2} (340 + v_B) = \frac{9}{16} (340 - v_B)$$8 (340 + v_B) = 9 (340 - v_B)$$2720 + 8v_B = 3060 - 9v_B$$17v_B = 340$$v_B = 20 \, m/s$

$A$ car $A$ is chasing another car $B$ with a speed of $20 \, m/s$,sounding a horn of frequency $180 \, Hz$. Both cars are moving towards a stationary siren of frequency $170 \, Hz$. What is the speed of car $B$ so that it does not hear any beats (in $, m/s$)? (Speed of sound $= 340 \, m/s$)

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