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

• 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

Answer 1

Answer: (D)

Given
$y_1=4\sin 600\pi t$
$y_2=5\sin 608\pi t$
Comparing with general equation
$y=a\sin 2\pi ft$
we get,
$f_1=300$
$f_2=304$
then,
Number of beats $=304-300=4$ beats $/\sec$
Intensity ratio is given as,
$\frac{I_{\max }}{I_{\min }}={\left(\frac{a_1+a_2}{a_1-a_2}\right)}^2$
$\frac{I_{\max }}{I_{\min }}={\left(\frac{4+5}{4-5}\right)}^2$
$\frac{I_{\max }}{I_{\min }}=\left(\frac{81}{1}\right)$
$\therefore I_{\max }:I_{\min }=81:1$