Question

When a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant ______.

Options

• Kinetic energy

• Potential energy

• Sum of kinetic energy and potential energy

• Difference between kinetic energy and potential energy

Answer 1

When a longitudinal wave propagates through a medium, the particles of the medium execute simple harmonic oscillations about their mean positions. These oscillations of a particle are characterised by an invariant sum of kinetic energy and potential energy.

Explanation:

When a particle executes Simple Harmonic Motion (SHM), its kinetic energy (KE) and potential energy (PE) are constantly changing:

• Kinetic energy is at its maximum at the mean position and zero at the extreme positions.
• Potential energy is zero at the mean position and reaches its maximum at the extreme positions.

However, according to the law of conservation of energy, the total mechanical energy, which is the sum of KE and PE, remains constant (invariant) at every point during the oscillation, provided there are no resistive forces like friction.