Wave Mechanics Question 676
Question: Two sources of sound placed close to each other are emitting progressive waves given by $ y _{1}=4\sin 600\pi t $ and $ y _{2}=5\sin 608\pi t $ . An observer located near these two sources of sound will hear:
Options:
A) 4 beats per second with intensity ratio 25 : 16 between waxing and waning.
B) 8 beats per second with intensity ratio 25 : 16 between waxing and waning
C) 8 beats per second with intensity ratio 81: 1 between waxing and waning
D) 4 beats per second with intensity ratio 81 : 1 between waxing and waning
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ 2\pi f _{1}=600\pi $
$ f _{1}=300 $ … (i) $ 2\pi f _{2}=608\pi $
$ f _{2}=304 $ …(ii) $ | f _{1}-f _{2} |=4,beats $
$ \frac{{I _{\max }}}{{I _{m.n.}}}=\frac{{{(A _{1}+A _{2})}^{2}}}{{{(A _{1}+A _{2})}^{2}}}=\frac{{{(5+4)}^{2}}}{{{(5-4)}^{2}}}=\frac{81}{1} $ where $ A _{1} $ , $ A _{2} $ are amplitudes of given two sound wave.
BETA
