A drone fitted with a siren is flying directl | vedclass

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Question

(C) The drone acts as a moving source of sound approaching a stationary reflecting surface (the building).
Given:
Speed of drone (source), $v_s = 15

Vedclass · Accepted Answer

$816$

Vedclass · Answer

(C) The drone acts as a moving source of sound approaching a stationary reflecting surface (the building).
Given:
Speed of drone (source), $v_s = 15 \,m/s$
Actual frequency, $n_0 = 780 \,Hz$
Speed of sound, $v = 340 \,m/s$
Step $1$: Calculate the frequency of the sound waves reaching the building.
Since the source is moving towards the stationary building, the frequency $n'$ received by the building is given by the Doppler effect formula:
$n' = n_0 \left( \frac{v}{v - v_s} \right)$
$n' = 780 \left( \frac{340}{340 - 15} \right) = 780 \left( \frac{340}{325} \right) = 816 \,Hz$
Step $2$: The building acts as a stationary source reflecting this frequency $n'$ back to the operator.
Since the operator is stationary and the building (acting as the source of the echo) is stationary, the frequency heard by the operator is the same as the frequency incident on the building.
Therefore, the frequency heard by the operator is $816 \,Hz$.

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