A standing wave of time period `T` is set up in a string clamped between two rigid supports, At `t =0` antinode is at its maximum displacement `2A`.

Options

A. The energy density of a node is equal to energy density of an antinode for the first time at `t= T//4`
B. The energy density of node and antinode becomes equal after `T//2` second
C. The displacement of the particle at antinode at `t = (T)/(8)` is `sqrt(2) A`
D. The displacement of the particle at node is zero

Answer

C, D

Explanation

Equation of `SHM` of particle who is at antinode is `y=2A sin ((2pi)/(T))t` at time `t=(T)/(8)`
`y=2A sin (pi)/(4)= sqrt(2)A`, Displacement of particle at note is always zero.