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 \[\frac{\pi }{3}\] 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 is 1 meter [BVP 2003]

• A.            2a  
• B.            \[a\sqrt{3}\]
• C.            \[a\sqrt{2}\]                         
• D.            a