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? (v is the velocity of sound)

• A. $\frac{v}{2}$
• B. $3v$
• C. 2V
• D. V

Answer 1

The correct option is D

V

Doppler Effect:

The variation in the frequency of sound caused by clear mobility between the origin and observer is known as Doppler's effect.

Step 1: Given

Velocity of source,$V_S$ = $0$,

Velocity of sound $V$ = $V$,

Apparent frequency $v\text{'}$= $2v$,

Actual frequency=$v$

We have to calculate the Velocity of the observer $V_0=?$

Step 2: Formula Used

The apparent frequency is given by the formula $v\text{'}=v\left(\frac{V+V_0}{V-V_S}\right)\dots \left(i\right)$,

Where $v\text{'}$ is Apparent frequency,

$v$ is the actual frequency,

$V_0$ is the velocity of the observer,

$V_S$ is the velocity of the source and

$V$ being the velocity of sound.

Step 3: Find the velocity of the observer, $V_0$

Substituting the given values in eq$\left(i\right)$,

$$\begin{gathered} v\text{'}=v\left(\frac{V+V_0}{V-V_S}\right) \\ \Rightarrow 2v=v\left(\frac{V+V_0}{V}\right) \\ \Rightarrow 2V=V+V_0 \\ \Rightarrow V=V_0 \end{gathered}$$

Thus, option D is correct.