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BITSAT2016PhysicsWaves and SoundActual

A source of sound S emitting waves of frequency 100 ~Hz and an observor O are located at some distance from each other. The source is moving with a speed of 19.4 ~ms ⁻¹ at an angle of 60^ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air 330 ~ms ⁻¹ )

Options

  1. A103 ~Hz
  2. B106 ~Hz
  3. C97 ~Hz
  4. D100 ~Hz

Correct answer

A. 103 ~Hz

Step-by-step solution

Here, original frequency of sound, f ₀=100 ~Hz Speed of source V_ s =19.4 60^ =9.7 From Doppler's formula f ^ l = f ₀ ( V - V ₀ ~V - V _ s ) f ^ l =100 ( V -0 ~V -(+9.7) ) f ^ l =100 V V (1- 9.7 ~V ) f ¹=100 (1+ 9.7 330 )=103 ~Hz Apparent frequency f ¹=103 ~Hz

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