Question

If a source approaches and recedes from observer with same velocity, the ratio of frequencies (apparent) is $6 : 5$, then velocity of source is: $ (v_{s}=330\,m/s) $

• A. 20 m/s
• B. 10 m/s
• C. 30 m/s
• D. 33 m/s

Answer 1

Answer: (C)

From Dopplers/effect, the perceived frequency when source approaches observer is
$ n=n\left( \frac{v}{v-v_{s}} \right) $ ..(i)
When source recedes the observer $= n$
$=n\left( \frac{v}{v+v_{s}} \right) $ ..(ii)
From Eqs. (i) and (ii), we get
$ \frac{n}{n\,}=\frac{v+v_{s}}{v-v_{s}} $
$ \frac{6}{5}=\frac{330+v_{s}}{330-v_{s}} $
$ \Rightarrow 1980-6v_{s}=1650+5v_{s} $
$ \Rightarrow 11v_{s}=1980-1650=330 $
$ v_{s}=\frac{330}{11}=30\,m/s $