Two harmonic waves are represented in SI units by
`y_1(x,t) = 0.2 sin (x-3.0t) and y_2(x,t) = 0.2 sin (x- 3.0t + phi)`
(a) Write the expression for the sum `y=y_1 + y_2 for phi = pi/2 rad.`
(b) Suppose the phase difference `phi` between the waves is unknown and the amplitude of their sum is 0.32 m, what is `phi`?

Answer

A, B, C, D

Explanation

(a) ` y= y_1 + y_2`
`= 0.2 sin (x-3.0t) + 0.2 sin (x-3.0t+ pi/2)`
`=A sin (x- 3.0t + theta)`

Here, A `= sqrt((0.2)^2 + (0.2)^2)`
and `theta = pi/4`
`:. y=0.28 sin (x-3.0t + pi/4)`
(b) Since, the amplitude of the resulting wave is
`0.32 m and A = 0.2 m`, we have
` 0.32 = sqrt((0.2)^2 + (0.2)^2 + (2)(0.2)(0.2) cos phi)`
Solving this, we get
`phi= +- 1.29` rad .