Two sources `S_1 " and "S_2` separated 2.0 m, vibrate according to equation `y_1= 0.03 sin pi t " and " y_2= 0.02 sin pi t " where "y_1, y_2` and t are in M.K.S unit. They send out waves of velocity 1.5 m/s. Calculate the amplitude of the resultant motion of the particle co-linear with `S_1 " and "S_2` and located at a point
In the middle of `S_2 " and "S_2`.

Explanation

The situation of shown in figure

The oscillations `y_1 " and "y_2` have amplitudes `A_1=0.03 m " and " A_2 = 0.02` respectively.
The frequency of both sources in `n = (omega)/(2pi)= (1)/(2) = 0.5 Hz`.
Now wavelength of each wave `lambda= (v)/(n)= (1.5)/(0.5) = 3.0 m`
For a point Q, between `S_1" and "S_2` the path difference is zero i.e., `phi =0`. Hence costructive interference take place at Q, thus amplitude at this point is maximum and given as
`R= sqrt(A_(1)^(2)+A_(2)^(2)+2A_1A_2)`
`=A_1+A_2= 0.03+0.02= 0.05` m.