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  4. 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 :

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

Waves

Solution:

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 $2\, Hz$.