If two sound waves, `y_1 = 0.3 sin 596 pi [t - x//330]` and `y_2 =0.5 sin 604 pi[t - x//330]` are superposed, what will be the (a) frequency of resultant wave (b) frequency at which the amplitude of resultant waves varies (c ) frequency at which beats aer produced. Find also the ratio of maximum and minimum intensities of beats.

Explanation

Comparing the given wave equation with
`y =A sin(ometat - kx) = A sin omega [t - (x //v)]`
`[as k//omega =I//v]`
we find that here `A_1 = 0.3 and omega_1 = 2pi f_1 =596 pi`
`i.e., f_1 =298 Hz and A_2 =0.5 and omega_2 =2 pi f_2 = 604 pi`
`i.e., f_2 = 302 Hz`
So (a) The frequency of the resultant wave
`f_(av) =(f_1 + f_2)/(2) = ((298+302))/2 = 300 Hz`
(b) The frequency at which amplitude of resultant
wave varies : `f_A =(f_1 + f_2)/(2) =((298 - 302))/2 =2Hz`
(c ) The frequency at which beats are produced `f_b = 2f_A = f_1 = f_2 = 4Hz`
(d) The ratio of maximum to minimum intensities of beat
`I_(max)/(I_(min)) =((A_1 + A_2)^2)/((A_1 - A_2)^2) =((0.3 + 0.5)^2)/((0.3 - 0.5)^2) =64/4 =16`