Question

With what velocity should an observer approach a stationary sound source, so that the apparent frequency of sound should appear double the actual frequency?

• A. \( \frac{v}{2} \)
• B. \( 3v \)
• C. \( 2v \)
• D. \( v \)

Hint:

When the observer moves towards a stationary sound source, the apparent frequency increases. To double the actual frequency, the observer must approach the source with a velocity equal to the speed of sound.

Answer 1

The Correct Option is D

The Doppler effect for sound gives the apparent frequency \( f' \) as: \[ f' = f \left( \frac{v + v_o}{v} \right) \] where:
- \( f' \) is the apparent frequency,
- \( f \) is the actual frequency,
- \( v \) is the speed of sound in air,
- \( v_o \) is the velocity of the observer. In this case, the observer is moving towards the stationary source, and we want the apparent frequency \( f' \) to be double the actual frequency \( f \). Hence: \[ 2f = f \left( \frac{v + v_o}{v} \right) \] Canceling \( f \) from both sides: \[ 2 = \frac{v + v_o}{v} \] Solving for \( v_o \): \[ 2v = v + v_o \quad \Rightarrow \quad v_o = v \]
Thus, the observer must approach the sound source with a velocity equal to the speed of sound \( v \). Therefore, the correct answer is: \[ \text{(4) } v \]