Question

The amplitude of a wave represented by equation `"y" = 1/(sqrt"a")  "sin"  omega"t" pm 1/(sqrt"b") "cos"  omega"t"` will be ____________.

Options

• `("a" + "b")/"ab"`

• `(sqrt"a" + sqrt"b")/"ab"`

• `(sqrt"a" pm sqrt"b")/"ab"`

• `sqrt(("a" + "b")/"ab")`

Answer 1

The amplitude of a wave represented by equation `"y" = 1/(sqrt"a")  "sin"  omega"t" pm 1/(sqrt"b") "cos"  omega"t"` will be `sqrt(("a" + "b")/"ab")`.

Explanation:

`"y" = 1/sqrt"a"  "sin"  omega"t" pm 1/sqrt"b" "sin" (omega"t" + pi/2)`

`"Here phase difference" = pi/2`

The resultant amplitude

`= sqrt((1/sqrt"a")^2 + (1/sqrt"b")^2)`

`= sqrt(1/"a" + 1/"b")`

` = sqrt(("a" + "b")/"ab")`