Question

With what velocity should an observer approach stationary sound source, so that the apparent frequency of sound appear to be double of the initial frequency? (given velocity of sound $= v$)

• A. $v_{o}=\frac{v}{2}$
• B. $v_{o}=3v$
• C. $v_{o}=2v$
• D. $v_{o}=v$

Answer 1

Answer: (D)

$v_{o}=v$

Answer 2

From Doppler?s effect, the perceived frequency is given by
$f'=f\left(\frac{v \pm v_{o}}{v \pm v_{s}}\right)$
where $f$ is original frequency, $v_{o}$ the velocity of observer,
$v_{s}$ of source and $v$ of sound.
Given, $v_{s}=0,\, f_{1}=f,\, f_{2}=2 f$
$\therefore s 2 f=f\left(\frac{v+v_{o}}{v+0}\right)$
$\Rightarrow v_{o}=v$