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KVPY2018PhysicsWaves and Sound

A person in front of a mountain is beating a drum at the rate of 40 per minute and hears no distinct echo. If the person moves 90   m closer to the mountain, he has to beat the drum at 60 per minute to not hear any distinct echo. The speed of sound is

Options

  1. A320   m s - 1
  2. B340   m s - 1
  3. C360   m s - 1
  4. D380   m s - 1

Correct answer

C. 360   m s - 1

Step-by-step solution

As drummer does not hear any echo this means time between two successive wavefronts is equal to time in which a wavefront reaches back to drummer. Distance covered by sound = 2 x If v = speed of sound, then 2 x v = time interval between two successive wavefronts. So, we have In case I, 2 x v = 60 40 ...( i ) In case II, 2 ( x - 90 ) v = 60 60 ... ( ii ) Substituting for x from Eq. ( i ) in Eq. ( ii ), we get 2 x - 180 = v ⇒ 3 2 v - 180 = v ⇒ v = 360 m s - 1

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