A standing wave in a string clamped between two rigid supports vibrate with time period T. For an antinode displacement is at its maximum at t = 0, is 2A. Choose the correct statement.

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The energy density of a node is equal to energy density of an antinode for the first time at t=T4

The energy density of node and antinode becomes equal after T2 seconds

The displacement of the particle at antinode at t=T8 is 2A

The displacement of the particle at node is non zero.

answer is C.

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Detailed Solution

The particle at antinode attains the maximum amplitude possible in the standing wave.Also, the displacement of particle at node is always zero.Equation of SHM of particle which is at antinode is given as y=2Asin⁡2πTt Substituting t=T8 in the equation, we get displacement y=2Asinπ4=2A

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