Question

If two waves represented by `"y"_1 = 3  "sin" omega "t"` and `"y"_2 = 5  "sin" (omega "t" + pi/3)` interfere at a point, then the amplitude of the resulting wave will be about ____________.

Options

• 7

• 6

• 5

• 3.5

Answer 1

If two waves represented by `"y"_1 = 3  "sin" omega "t"` and `"y"_2 = 5  "sin" (omega "t" + pi/3)` interfere at a point, then the amplitude of the resulting wave will be about 7.

Explanation:

`phi = pi/3,`

Let a₁ and a₂ be amplitudes of two waves.

`therefore "a"_1 = 3, "a"_2 = 5`

`"Resultant amplitude, a" = sqrt("a"_1^2 + "a"_2^2 + 2  "a"_1 "a"_2  "cos" phi)`

`therefore "a" = 7`