Two vibrating tuning forks produce progressive waves given by , `y_(1) = 4 sin (500 pi t) and y_(2) = 2 sin (506 pi t)`. These tuning forks are held near the ear of person . The person will hear

Options

A. 3 beats/s with intensity ratio of maxima to minima `=9`
B. 3 beats/s with intensity ratio of maxima to minima `=2`
C. 6 beats/s with intensity ratio of maxima to minima `=2`
D. 6 beats/s with intensity ratio of maxima to minima `=9`

Answer

A

Explanation

Comparing given equations with
`y=Asin omegat`
`A_(1)=4,omega_(1)=500pi`
`A_(2)=2,omega_(2)=506pi`
`v_(1)=(omega_(1))/(2pi)=250`
`v_(2)=(omega_(2))/(2pi)=253`
Number of beats `v_(2)-v_(1)`
`=253-250=3`
`(l_("max"))/(l_("min"))=((A_(1)+A_(2))^(2))/((A_(1)-A_(2))^(2))=((4+2)^(2))/((4-2)^(2))=9/1`