Q. Two sounding bodies producing progressive waves are given by $y_{1} = 4\sin{400\pi t\ and\ y_{2} = 3\sin{404\pi t}}$ one situated very near to the ear of a person who will hear
A) 2 beats/s with intensity ratio 4/3 between maxima and minima
B) 2 beats/s with intensity ratio 49/1 between maxima and minima
C) 4 beats/s with intensity ratio 4/3 between maxima and minima
D) 4 beats/s with intensity ratio 4/3 between maxima and minima
Explanation
(b) $n_{1} = \frac{\omega_{1}}{2\pi} = \frac{400\pi}{2\pi} = 200\ Hz\ $
$n_{2} = \frac{\omega_{2}}{2\pi} = \frac{400\pi}{2\pi} = 202\ Hz$
∴ Number of beats per sec $n = n_{2} - n_{1} = 2$
Again, $A_{1} = 4\ and\ A_{2} = 3\ $
$\frac{I_{\max\ }}{I_{\min\ }} = \frac{\left( A_{1} + A_{2} \right)^{2}}{\left( A_{1} - A_{2} \right)^{2}} = \left( \frac{4 + 3}{4 - 3} \right)^{2} = \frac{49}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.