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Equation of a plane wave is given by 4 s...

Equation of a plane wave is given by `4 sin .(pi)/(4)[2t+(x)/(8)]`. The phase difference at any given instant of two particles 16 cm apart is

A

`60^(@)`

B

`90^(@)`

C

`30^(@)`

D

`120^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y = 4 sin. (pi)/(4) (2t+(x)/(8)) " "….(i)`
or `y = 4 sin((pi)/(2)t + (pix)/(32))" "….(ii)`
The standard equation is
`y = 4 sin (omega t pm kx)`
Comparing the Eq. (i) with Eq. (ii), we get
` k = (pi)/(2)`
`therefore " "(2pi)/(lambda)=(pi)/(32)`
`therefore " "(lambda)/(2)=32`
`therefore " "lambda = 64`
`therefore " "Delta phi = (2pi)/(lambda)Deltax`
`= (2pi)/(64) xx 16 = (pi)/(2) = 90^(@)`
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