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# A cliff emits a sound of frequency $1000\,Hz$ , it moves away from the observer towards a cliff with a speed of $10m{s^{ - 1}}$ . Then the frequency of sound heard by observer coming directly from the siren is:A. Less than $1000\,Hz$B. Greater than $1000\,Hz$C. Equal to $1000\,Hz$D. No sound is heard

Last updated date: 19th Jul 2024
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Hint: Here we have to use the principle of Doppler Effect of sound.
Doppler Effect of sound: The Doppler effect is the difference in a wave’s frequency in response to an observer that shifts relative to the source of the wave. The change of pitch heard as a vehicle with a horn approaches and retreats from an observer is a typical example of Doppler Effect.

Speed of the siren sound $= 10m{s^{ - 1}}$
We know that,
Speed of sound in air $= 330m{s^{ - 1}}$
Let ${f_ \circ }$
be the frequency of the sound originally emitted from the siren
Let $f$
be the frequency of the siren when it is moving away from the observer.
Since, distance between the cliff and siren is decreasing,
So, $f < {f_ \circ }$
$f = {f_ \circ }\left( {\dfrac{v} {{v + {v_s}}}} \right) \\ f = \left( {\dfrac{{330}} {{330 + 10}}} \right) \times 1000 \\ f = \dfrac{{33}} {{34}} \times 1000 \\$
Since, the answer is less than $1000\,Hz$
So, the correct option is A.