Wave Mechanics Question 674
Question: In the figure shown the wave speed is v. The velocity of car is $ v _{0} $ . The beat frequency for the observer will be
Options:
A) $ \frac{2f _{0}vv _{0}}{v^{2}+v _{0}^{2}} $
B) $ \frac{2f _{0}v^{2}}{v^{2}-v _{0}^{2}} $
C) $ \frac{2f _{0}vv _{0}}{v^{2}-v _{0}^{2}} $
D) $ \frac{f _{0}vv _{0}}{v^{2}-v _{0}^{2}} $
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Answer:
Correct Answer: C
Solution:
[c] $ f _{2}=\frac{f _{0}v}{v+v _{0}} $ The wave which reaches wall $ f _{1} $ is reflected. $ f _{1}=\frac{f _{0}v}{v-v _{0}} $ The reflected frequency is $ f _{1} $ as the wall is at rest. Beats $ =f _{1}-f _{2}=\frac{f _{0}v}{v-v _{0}}-\frac{f _{0}v}{v+v _{0}}=\frac{2f _{0}vv _{0}}{v^{2}-v _{0}^{2}} $
BETA
