The two individual wave functions are `y_(1)=(5" cm")sin (4x-t)and y_(2)=(5" cm") sin (4x + t)` where, x and y are in centimetres. Find out the maximum displacement of the motion at ` x = 2.0` cm.

Options

A. `9.89` cm
B. 8 cm
C. `8.39` cm
D. `7.69` cm

Answer

a

Explanation

Given, `y_(1)=(5" cm")sin (4x-t)and y_(2)=(5" cm") sin (4x + t)`
We know `y=(2A sin kx )cos omegat`
Compare `y_(1)=(5" cm") sin (4x-t)` with `y_(1) = A sin (kx-omegat)`
`A=5, k=4 and omega = 1`
`Now, " y"_("max") = 10 sin 4x|_(x=2.0,`
`10 xx sin (4xx2) = 10 sin (8xx(180^(@))/pi)`
`rArr " y"_("max")=9.89" cm"`