To understand why the correct answer is option 'C', let's break down the problem and use the Doppler effect formula to solve it.

1. Understanding the Doppler Effect:
The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave. It is commonly experienced with sound waves when a sound source and an observer are in relative motion.

2. Apparent Frequency and Actual Frequency:
The apparent frequency is the frequency of the sound wave as observed by the stationary observer, while the actual frequency is the frequency of the sound wave emitted by the moving source.

3. Doppler Effect Formula:
The formula to calculate the apparent frequency (fa) given the actual frequency (f), velocity of the source (vs), and velocity of sound (v) is:

fa = f * (v + vo) / (v + vs)

where:
fa = apparent frequency
f = actual frequency
v = velocity of sound
vo = velocity of observer (assumed to be zero in this case)
vs = velocity of source

4. Solving the Problem:
In this case, the observer is stationary (vo = 0), and the apparent frequency is double the actual frequency (fa = 2f). We need to find the velocity of the source (vs).

Using the Doppler effect formula, we can substitute the given values:

2f = f * (v + 0) / (v + vs)

Simplifying the equation:

2 = v / (v + vs)

Cross-multiplying:

2(v + vs) = v

Expanding:

2v + 2vs = v

Rearranging the equation:

2vs = -v

Dividing by 2:

vs = -v / 2

Since velocity cannot be negative in this context, we take the magnitude:

vs = v / 2

Therefore, the velocity of the sound source should be half the velocity of sound (v) in order for the apparent frequency to be double the actual frequency.

Hence, the correct answer is option 'C' (v/2).