Two sources of sound placed close to each other, are emitting pro… - Vidyadip

MCQ

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

A
$8$ beats per second with intensity ratio $81\,\,:\,\,1$ between waxing and waning
✓
$4$ beats per second with intensity ratio $81\,\,:\,\,1$ between waxing and waning
C
$4$ beats per second with intensity ratio $25\,\,:\,\,16$ between waxing and waning
D
$8$ beats per second with intensity ratio $25\,\,:\,\,16$ between waxing and waning

✓

Answer

Correct option: B.

$4$ beats per second with intensity ratio $81\,\,:\,\,1$ between waxing and waning

b
$f_{1}=300$

$\mathrm{f}_{2}=304$

$\therefore \mathrm{f}_{\mathrm{beat}}=\mathrm{f}_{2}-\mathrm{f}_{1}=304-300=4$

intensity ratio $=\frac{\mathrm{I}_{\max }}{\mathrm{I}_{\min }}=\frac{\mathrm{A}_{\max }^{2}}{\mathrm{A}_{\min }^{2}}=\frac{(4+5)^{2}}{(5-4)^{2}}=\frac{81}{1}$

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