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

The apparent frequency $f'$ heard by an observer moving towards a stationary source is given by the Doppler effect formula:

$f' = f \left( \dfrac{v + v_o}{v} \right)$

where $f$ is the actual frequency, $v$ is the speed of sound, and $v_o$ is the velocity of the observer.

Given that the apparent frequency is double the actual frequency, we have $f' = 2f$. Substituting this into the formula:

$2f = f \left( \dfrac{v + v_o}{v} \right)$

Dividing both sides by $f$:

$2 = \dfrac{v + v_o}{v}$

$2v = v + v_o$

$v_o = v$

Answer: $v$