A toy-car, blowing its horn, is moving with a steady speed of 5m s...

A toy-car, blowing its horn, is moving with a steady speed of

5m{s}^{- 1}

, away from a wall. An observer, towards whom the toy car is moving, is able to hear

5

beats per second. If the velocity of sound in air is

340m{s}^{- 1}

the frequency of the horn of the toy car is close to

Options

A $680Hz$
B $510Hz$
C $340Hz$
D $170Hz$

Correct answer

D. $170Hz$

Step-by-step solution

$\text{Frequency heard by\text{ the } observer directly from source}f\left(\dfrac{340}{340 - 5}\right) = {f}_{1}$

$\text{Frequency heard by\text{ the }\text{ observer }\text{ coming }\text{ after }\text{ relection }\text{ from }\text{ wall }}$
$f \left(\dfrac{340}{340 + 5}\right)= {f}_{2}<br /><br />Beats frequency$ = \left({f}_{1} - {f}_{2}\right)

$5 = f \left(\dfrac{340}{340 - 5} - \dfrac{340}{340 + 5}\right)$

$⇒ f = 170$ & Hz

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