Two waves
` y_(1) =A_(1) sin (omega t - beta _(1)), y_(2)=A_(2) sin (omega t - beta_(2)`
Superimpose to form a resultant wave whose amplitude is

Options

A. `sqrt(A_(1)^(2)+A_(2)^(2)+A_(1)A_(2)cos(beta_(1)-beta_(2)))`
B. `sqrt(A_(1)^(2)+A_(2)^(2)+A_(1)A_(2)sin(beta_(1)-beta_(2)))`
C. `A_(1)+A_(2)(4)|A_(1)+A_(2)|`
D. -

Answer

A

Explanation

`phi=(omegat-beta_(2))-(omegat-beta_(1))=(beta_(2)-beta_(1))`
`:. A=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cos(beta_(2)-beta_(1)))`