They oscillate up and down about their mean position perpendicular to the wave propagation.
Explanation
Mechanical waves are classified based on the direction of particle oscillation relative to the direction of wave propagation. The two primary types are transverse waves and longitudinal waves.
Analysis of Options:
- They oscillate back and forth parallel to the direction of wave propagation. is incorrect: Oscillation back and forth parallel to the direction of wave propagation characterizes longitudinal waves (e.g., sound waves in air). In these waves, the medium undergoes compression and rarefaction.
- They oscillate up and down about their mean position perpendicular to the wave propagation. is correct: In a transverse wave, particles of the medium oscillate up and down about their mean position, perpendicular (at 90 degrees) to the direction in which the wave travels. Examples include waves on a string, ripples on water surfaces, and electromagnetic waves (though EM waves do not require a material medium).
- They travel along with the wave from the source to the receiver. is incorrect: In wave motion, the particles of the medium do not travel from the source to the receiver. Only energy and momentum are transferred. The particles merely oscillate around a fixed equilibrium position.
- They remain stationary while the energy passes through them. is incorrect: Particles are not stationary; they must oscillate to transmit the disturbance (energy) through the medium.
Key Takeaway:
The defining characteristic of a transverse wave is that particle motion is perpendicular to the direction of wave propagation, whereas in a longitudinal wave, particle motion is parallel to the direction of propagation.