Question

Choose the correct alternative(s) regarding standing waves in a string

• A. particles near the antinode have lesser potential energy than the particles near the node when they reaches at its extreme position
• B. All the particles crosses their mean position simultaneously
• C. Energy and momentum can transmitted through node
• D. Particles near the antinode have lesser kinetic energy than the particles near the node when they crosses their mean position

Answer 1

Answer: (A), (B)

The correct options are
A particles near the antinode have lesser potential energy than the particles near the node when they reaches at its extreme position
B All the particles crosses their mean position simultaneously

At the antinode, the tension and hence the elongation in the string in minimum and hence minimum potential energy. While at the nodes, tension is maximum and hence maximum potential energy. All particles perform SHM with same time period and hence since the phase differecnce between any two particles is constant, they cross mean position simultaneously.

As note is always at rest, energy and momentum cannot be transferred through it.

Particles at antinode have maximum velocity and hence maximum kinetic energy while crossing the mean position.