Question

Two waves are represented by the equations `"y"_1, = "a sin" (omega"t"+ "kx" + 0.57)` m and `"y"_2, = "a cos" (omega"t"+ "kx")` m, where x is in metre and t in second. The phase difference between them is ____________.

Options

• 1.0 radian

• 1.25 radian

• 1.57 radian

• 0.57 radian

Answer 1

Two waves are represented by the equations `"y"_1, = "a sin" (omega"t"+ "kx" + 0.57)` m and `"y"_2, = "a cos" (omega"t"+ "kx")` m, where x is in metre and t in second. The phase difference between them is 1.0 radian.

Explanation:

We know that,

 `"y"_1, = "a sin" (omega"t"+ "kx" + 0.57)`    .....(i)

`"y"_2, = "a cos" (omega"t"+ "kx")`

`"y"_2 = "a sin" (omega"t" + "kx" + pi//2)  "m"`    .....(ii)

From the above equations, we get

`phi_1 = 0.57`

`phi_2 = 3.14/2 = 1.57`

`therefore "Phase difference,"  phi = phi_2 - phi_1`

` = 1.00  "radian"`