Question

Two waves are given as y₁ = 10 sin ωt cm and y₂ = 10 sin `(omegat + pi/3)` cm are superimposed. What is the amplitude of the resultant wave? `[cos  pi/3 = 1/2]`

Options

• `10sqrt2` cm

• `5sqrt3` cm

• `10sqrt3` cm

• 10 cm

Answer 1

`underline(10sqrt3  "cm")`

Explanation:

Both the waves have an amplitude equal to 10 cm. The phase difference between them is `pi/3`.

The resultant amplitude is given by

A = `sqrt(A_1^2 + A_2^2 + 2A_1A_2 costheta)`

= `sqrt((10)^2 + (10)^2 + 2 xx 10 xx 10 xx cos  pi/3)`

= `sqrt(3 xx 10^2) = 10sqrt3` cm