Two sounding bodies are producing progressive wave given by y1=4 sin (400 π t) and y2=3 sin (404 π t), where t is in second which superpose near the ears of a person. The person will heat :

Question

Two sounding bodies are producing progressive wave given by y1=4 sin (400 π t) and y2=3 sin (404 π t), where t is in second which superpose near the ears of a person. The person will heat : (A) 2 beats per second with intensity ratio (4/3) between maxima and minima (B) 2 beats per second with intensity ratio 49 between maxima and minima (C) 4 beats per second with intensity ratio 7 between maxima and minima (D) 4 beats per second with intensity ratio (4/3) between maxima and minima

Tardigrade Admin · Accepted Answer

When the two waves superpose then the maximum amplitude will be 4+3=7 and minimum will be 4-3=1 hence the ratio of maximum to minimum intensity will be 49 and as the frequencies of the two waves are 200 Hz and 202 Hz the beat frequency will be 2 Hz.

Q. Two sounding bodies are producing progressive wave given by $y_{1} = 4 sin (400 π t)$ and $y_{2} = 3 sin (404 π t)$ , where $t$ is in second which superpose near the ears of a person. The person will heat :

2 beats per second with intensity ratio $\frac{4}{3}$ between maxima and minima

2 beats per second with intensity ratio 49 between maxima and minima

4 beats per second with intensity ratio 7 between maxima and minima

4 beats per second with intensity ratio $\frac{4}{3}$ between maxima and minima

When the two waves superpose then the maximum amplitude will be $4 + 3 = 7$ and minimum will be $4 - 3 = 1$ hence the ratio of maximum to minimum intensity will be $49$ and as the frequencies of the two waves are $200 Hz$ and $202 Hz$ the beat frequency will be $2 Hz$ .

Q. Two sounding bodies are producing progressive wave given by y1​=4sin(400πt) and y2​=3sin(404πt), where t is in second which superpose near the ears of a person. The person will heat :

2 beats per second with intensity ratio 34​ between maxima and minima