Two sound waves each of wavelength `lamda` and having the same amplitude A form two sources `S_(1) and S_(2)` interfere at a point P. If the path difference `S_(2)P - S_(1)P = (lamda)/(3)`, then the amplitude of the resultant were at P will be

Options

A. A
B. 2A
C. A/2
D. 3A/2

Answer

A

Explanation

Path diff.= `(lamda)/(3)`
`:.` Phase diff. `= (2pi)/(lamda) xx (lamda)/(3) = (2pi)/(3) = 120^(@)`
Resultant amplitude
`R = sqrt(A^(2) + A^(2) + 2A^(2) cos 120^(@))`
`:. R = sqrt(2A^(2) - 2A^(2) xx (1)/(2)) = A`