Two vibrating tuning forks produce waves given by
`y_(1)=4 sin 53 pi t, y_(2)=2 sin 50 pi t`
If they are held near the ear of a person, the person will hear

Options

A. 3 beats `s^(-1)` with intensity ratio of maximum to minima equal to 9
B. 3 beats `s^(-1)` with intensity ratio of maxima to minima equal to 2
C. 6 beats `s^(-1)` with intensity ratio of maxima to minima equal to 2
D. 6 beats `s^(-1)` with intensity ratio of maxima to minima equal to 9

Answer

B

Explanation

`y_(1) = 4 sin 53pi t and y_(2) = 2 sin 50pi t`
`:. A_(1) = 4 f_(1) = 53`
`A_(2) = 2 f_(2) = 50`
`:.` Beat `= 53 - 50 = 3 "sec"^(-1)`
`(l_("max"))/(l_("min")) = ((A_(1) + A_(2))^(2))/((A_(1) - A_(2))^(2)) = ((4 + 2)^(2))/((4 -2)^(2)) = (36)/(4) = 9 : 1`