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=4sin\left( {600\pi t} \right)$ and $y_2=5sin\left( {608\pi t} \right)$ An observer located near these two sources of sound will hear

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.
✓
$4$ beats per second with intensity ratio $81 : 1$ between waxing and waning.

✓

Answer

Correct option: D.

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

d
$\text { Given }: y_{1}=4 \sin 600 \pi t, y_{2}=5 \sin 608 \pi t$

$\therefore \quad \omega_{1}=600 \pi$ or $2 \pi v_{1}=600 \pi$ or $v_{1}=300$

$A_{1}=4$

and $\omega_{2}=608 \pi$ or $2 \pi \mathrm{v}_{2}=608 \pi$ or $\mathrm{v}_{2}=304$

$A_{2}=5$

Number of beats heard per second

$=v_{2}-v_{1}=304-300=4 $

$\frac{I_{\max }}{I_{\min }}=\frac{\left(A_{1}+A_{2}\right)^{2}}{\left(A_{1}-A_{2}\right)^{2}}=\frac{(4+5)^{2}}{(4-5)^{2}}=\frac{81}{1}$

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