Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is `a` and the phase of A is ahead by `pi//3` than that of B and the distance AP is greater than BP by `50 cm`. Then the resultant amplitude at the point P will be if the wavelength `1` meter

Options

A. 2a
B. `asqrt(3)`
C. `asqrt(3)`
D. a

Answer

D

Explanation

Path difference `(Deltax) = 50 cm = (1)/(2)m`
Phase difference
implies `Deltaphi = (2pi)/(lambda) xx Deltax implies phi = (2pi)/(1) xx (1)/(2) = pi`
Total phase difference = `pi - (pi)/(3) = (2pi)/(3)`
implies ` A = sqrt(a^(2)+ a^(2) + 2a^(2) cos(2pi//3)) = a`