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COMEDK2022PhysicsWaves and Sound

A source of sound emits sound waves at frequency f₀ . It is moving towards an observer with fixed speed v_s (v_s The variation of f with v₀ is given correctly by

Options

  1. Agraph A with slope = f₀ (v+v_s )
  2. Bgraph B with slope = f₀ (v-v_s )
  3. Cgraph A with slope = f₀ (v-v_s )
  4. Dgraph B with slope = f₀ (v+v_s )

Correct answer

C. graph A with slope = f₀ (v-v_s )

Step-by-step solution

According to the Doppler effect, when a source of sound moving with speed v_s towards a stationary observer emits sound of frequency f₀ , and the observer moves towards the source with speed v₀ , the observed frequency f is given by the formula: f = f₀ ( v + v₀ v - v_s ) where v is the speed of sound in air. This equation can be rewritten as: f = ( f₀ v - v_s ) v₀ + ( f₀ v v - v_s ) This is a linear equation of the form f = mv + c , where m is the slope and c is the y-intercept. Comparing the terms, the slope m is

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