Question

Two vibrating tuning fork produce progressive waves given by `y_(1)=4 sin(500 pit)` and `y_(2)=2 sin(506 pi t)`. These tuning forks are held near the ear of a person. The person will hear `alpha` beats/s with intensity ratio between maxima and minima equal to `beta`. Find the value of `beta-alpha`.

Answer 1

Correct Answer - 6
`y_(1)=4 sin(500 pit) y_(2)=2 sin(506 pit)`
Number of beats `= (n_(1)-n_(2))/(2)=(506-500)/(2)=3` beat/sec
As `I_(1) prop(16)` and `I_(2) prop 4 rArr (I_(max))/(I_(min))=((sqrt(I_(1))+sqrt(I_(2)))^(2))/((sqrt(I_(1))-sqrt(I_(2)))^(2)) rArr ((4+2)/(4-2))^(2)=((6)/(2))^(2)=9`.