question_answer

If a sources approaches and recedes from observer with same velocity, then the ratio of frequencies (apparent) is 6 : 5, then velocity of source is: \[({{V}_{s}}=300m/s)\]

A) 20m/s                           

B) 10m/s

C) 30m/s                           

D) 33m/s

Correct Answer: C

Solution :

[c] When source approaches observer \[{{f}_{1}}={{f}_{{}^\circ }}\frac{V}{V-{{V}_{sourec}}}\] \[{{f}_{1}}={{f}_{{}^\circ }}\frac{330}{330-{{V}_{sourec}}}....(1)\] When source recedes from observer \[{{f}_{1}}={{f}_{{}^\circ }}\frac{V}{V+{{V}_{sourec}}}\] \[{{f}_{1}}={{f}_{{}^\circ }}\frac{330}{330-{{V}_{sourec}}}....(2)\] \[\frac{{{f}_{1}}}{{{f}_{2}}}=\frac{6}{5}=\frac{330+{{V}_{source}}}{330-{{V}_{source}}}\] \[6\,[330-{{V}_{source}}]\,=5\,[330+{{V}_{source}}]\] \[1980-6{{V}_{source}}=1650+5{{V}_{source}}\] \[330=11{{V}_{source}}\] \[{{V}_{source}}=30\,m/s\]