Two identical sinusoidal waves are moving in the same direction along a stretched string, interfere with each other. The phase difference between them is `120^(@). The amplitudes of both the waves are same. If the amplitude of the resultant wave due to interfernce is 2mm, the amplitude of each wave is

Options

A. 1mm
B. 2mm
C. `sqrt3 mm`
D. `2sqrt3mm`

Answer

B

Explanation

Given amplitude of each sinusoidal waves are same.
i.e., `a_(1)=a_(2)=a`
phase difference, `phi=120^(@)`
Resultant amplitude, A=2 mm
`:'A=sqrt(a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)cos120^(@))`
`2=sqrt(a^(2)+a^(2)+2a^(2)(-(1)/(2)))`
`2=sqrt(a^(2)+a^(2)-a^(2))`
`2=sqrt(a^(2))`
2=a
or a=2mm
Hence, the amplitude of each wave is 2 mm.