If two sund 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 are 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`