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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

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Last updated date: 19th Jul 2024
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Answer
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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.

Complete step by step answer:Given,
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.

Additional information:
The Doppler Effect is caused when waves are transmitted out at a normal rate or frequency by the source of a waveform, such as sound or light, but there is continuous relative motion between the source and the observer, allowing frequency measured to change.
The explanation for Doppler Effect is that each subsequent wave crest is produced from a position closer to the observer than the crest of the previous wave as the wave source travels towards the observer. Thus, each wave takes significantly less time than the previous wave to enter the observer.

Note:Here we have to see whether the sound wave of the siren is decreasing from the observer or not. Then only we can apply the Doppler effect. Also we have to correctly remember the formula of the Doppler Effect otherwise the answer will be wrong.