Question

With what velocity should an observer move relative to a stationary source so that a sound of double the frequency of source is heard by an observer?

• A. Half the velocity of sound towards the source
• B. Same as velocity of sound away from the source
• C. Twice the velocity of sound towards the source
• D. Same as velocity of sound towards the source

Hint:

For a stationary source, frequency increases only due to observer’s motion towards the source.

Answer 1

The Correct Option is D

Step 1: Doppler effect formula for moving observer.
\[ f' = f\left(\frac{v + v_o}{v}\right) \] where \(v_o\) is observer’s velocity towards the source.

Step 2: Condition for doubled frequency.
\[ 2f = f\left(\frac{v + v_o}{v}\right) \]

Step 3: Solve for observer’s velocity.
\[ 2 = \frac{v + v_o}{v} \Rightarrow v_o = v \]