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:

  1. (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.