In which type of mechanical wave do particles of the medium vibrate in a direction perpendicular to the direction of wave propagation?

Introduction / Context:
Mechanical waves can be classified based on how particles of the medium move relative to the direction in which the wave travels. Understanding this distinction helps in analysing waves on strings, water surfaces, and sound in air. This question focuses on identifying the type of wave for which particle vibration is perpendicular to the direction of wave propagation.

Given Data / Assumptions:

• The wave is a mechanical wave requiring a material medium.
• Particles of the medium are said to vibrate at right angles to the direction in which the wave travels.
• Options include longitudinal, rolling, transverse, and field waves.
• We assume standard textbook definitions of these wave types.

Concept / Approach:
In a transverse wave, particles of the medium move perpendicular to the direction of energy transfer or wave propagation. A classic example is a wave on a stretched string, where the string moves up and down while the disturbance travels horizontally. In longitudinal waves, particles oscillate parallel to the direction of propagation, as in sound waves in air. Rolling and field waves are not standard basic categories in this context. Therefore, the correct classification for a wave with perpendicular particle motion is transverse wave.

Step-by-Step Solution:
Step 1: Recall that mechanical waves involve oscillations of particles about their mean positions. Step 2: Identify that the question specifies particle motion perpendicular to the wave direction, which is the defining feature of transverse waves. Step 3: Visualise a rope tied at one end; if you jerk the free end up and down, loops move along the rope, but each point on the rope moves vertically while the disturbance travels horizontally. Step 4: Compare this with a longitudinal wave like sound in air, where compressions and rarefactions move along the direction of propagation, and particles move back and forth along that same line. Step 5: Conclude that the correct type of wave for the described motion is a transverse wave.

Verification / Alternative check:
Check standard diagrams of transverse and longitudinal waves. In transverse wave diagrams, displacement is drawn vertically while the wave moves horizontally, emphasising the perpendicular relationship. Texts explicitly state that in transverse waves, particle displacement is perpendicular to the direction of propagation. No such description is given for longitudinal waves. Rolling and field waves are used in other contexts but are not the basic categories for simple mechanical waves in school level physics.

Why Other Options Are Wrong:
Longitudinal wave: Particles move parallel to the direction of propagation, as in sound waves, so this does not match perpendicular motion. Rolling wave: This term may appear in discussions of water surface motion but is not a standard basic category used in introductory definitions. Field wave: This is not a commonly defined mechanical wave type at this level and does not specifically describe particle motion.

Common Pitfalls:
Students often confuse the names because they associate longitudinal with long distances and transverse with crossing. A clearer strategy is to remember specific examples: light on a string is transverse, sound in air is longitudinal. Visualising particle motion with arrows helps fix the concept: perpendicular arrows for transverse waves and parallel arrows for longitudinal waves.

Final Answer:
The described wave, where particles vibrate perpendicular to the direction of propagation, is a transverse wave.