Question

Three waves of equal frequency having amplitudes `10mum`, `4mum`, `7mum` arrive at a given point with successive phase difference of `pi//2`, the amplitude of the resulting wave in `mum` is given by
A. (a) `4`
B. (b) `5`
C. (c) `6`
D. (d) `7`

Answer 1

Correct Answer - B
The amplitudes of the waves are
`a_1=10mum`, `a_2=4mum` and `a_3=7mum`
and the phase difference between 1st and 2nd wave is `pi/2` and that between 2nd and 3rd wave is `pi/2`. Therefore, phase difference between 1st and 3rd is `pi`. Combining 1st with 3rd, their resultant amplitude is given by
`A_1^2=a_1^2+a_3^2+2a_1a_3cos varphi`
or `A_1=sqrt(10^2+7^2+2xx10xx7cos pi)`
`=sqrt(100+49-140)`
`=sqrt9=3mum` in the direction of first.
Now combining this with 2nd wave we have, the resultant amplitude
`A^2=A_1^2+a_2^2+2A_1a_2cospi/2`
or `A=sqrt(3^2+4^2+2xx3xx4cos 90^@)=sqrt(9+16)`
`=5mum`