Waves - Result Question 55
57. 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 :
[2012]
(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
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Answer:
Correct Answer: 57. (d)
Solution:
- (d) $2 \pi f_1=600 \pi$
$f_1=300$
$2 \pi f_2=608 \pi$
$f_2=304$
$|f_1-f_2|=4$ beats
$\frac{I _{\max }}{I _{\min }}=\frac{(A_1+A_2)^{2}}{(A_1+A_2)^{2}}=\frac{(5+4)^{2}}{(5-4)^{2}}=\frac{81}{1}$
where $A_1, A_2$ are amplitudes of given two sound wave.
