Two sound waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is `120^(@)`. The resultant amplitude will be

Options

A. `sqrt(2)A`
B. 2A
C. 3A
D. A

Answer

A

Explanation

Here, `A_(1)=A,A_(2)=A,phi=120^(@)`
The amplitude of the resultant wave is
`A_(R)=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)=sqrt(A^(2)+A^(2)+2A Acos120^(@))`
`=sqrt(A^(2)+A^(2)-A^(2))=A" "(because cos120^(@)=-(1)/(2))`