When the listener moves towards stationary source with velocity ' V 1 ', the apparent frequency of emitted note is ' F 1 '. When observer moves away from the source with veloci

Question

When the listener moves towards stationary source with velocity ' V 1 ​ ', the apparent frequency of emitted note is ' F 1 ​ '. When observer moves away from the source with velocity ' V 1 ​ ', apparent frequency is ' F 2 ​ '. If' V is the velocity of sound in air and F 2 ​ F 1 ​ ​ = 2 then V 1 ​ V ​ is

TestHub · Accepted Answer

Using the Doppler effect formula, when the listener moves towards the stationary source, the apparent frequency is

$F_{1} = F (\frac{V + V _{1}}{V})$

When the listener moves away from the stationary source, the apparent frequency is

$F_{2} = F (\frac{V - V _{1}}{V})$

Given that $\frac{F _{1}}{F _{2}} = 2$ , we have

$\frac{V + V _{1}}{V - V _{1}} = 2$

$V + V_{1} = 2 V - 2 V_{1}$

$3 V_{1} = V$

$\frac{V}{V _{1}} = 3$

Answer: 3

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