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
$y=a \sin 2 \pi f t$
we get,
$f_{1}=300 $
$ f_{2}=304$
then,
Number of beats $=304-300=4$ beats $/ \sec$
Intensity ratio is given as,
$\frac{I_{\max }}{I_{\min }}=\left(\frac{a_{1}+a_{2}}{a_{1}-a_{2}}\right)^{2}$
$\frac{I_{\max }}{I_{\min }}=\left(\frac{4+5}{4-5}\right)^{2}$
$\frac{I_{\max }}{I_{\min }}=\left(\frac{81}{1}\right)$
$\therefore I _{\max }: I _{\min }=81: 1$