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

Answer

D

Explanation

Here `A_(1)=A,A_(2)=A, varphi=120^(@)`
The amplitude of the resulting wave is
`A_(R)=sqrt((A_(1))^(2)+(A_(2))^(2)+2A_(1)A_(2) cos varphi)`
`=sqrt(A^(2)+A^(2)+2 A A cos 120^(@))`
`= sqrt((A^(2)+A^(2)-A^(2)))=A ( :. cos120^(@)=-(1)/(2))`