Q. Two sources of sound placed 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
Explanation

(d) $2\pi\ f_{1} = 600\pi$
$f_{1}\ \ \ \ \ \ = 300$ …(i)
$2\pi\ f_{2} = 608\pi$
$f_{2}\ \ \ \ \ \ = 304$ …(ii)
$\left| f_{1} - f_{2} \right| = 4\ beats$
$\frac{I_{\max}}{I_{\min}} = \frac{\left( A_{1} + A_{2} \right)^{2}}{\left( A_{1} - A_{2} \right)^{2}} = \frac{(5 + 4)^{2}}{(5 - 4)^{2}} = \frac{81}{1}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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