Q.Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:

Key Idea: Wave Type Classification

The type of wave depends on the direction of particle displacement relative to the wave's propagation.

Reasoning Steps

1. Part (a): Displacing the spring end sideways creates a kink that moves along the spring. The coils move mainly sideways (perpendicular to the spring's length), but a "longitudinal" spring (a slinky-type coil) also transmits some of that disturbance along its own length as the coils bunch and stretch → real textbook answer: transverse and longitudinal (a combination).
2. Part (b): Moving the piston back and forth compresses and rarefies the liquid. Particles oscillate parallel to the piston's motion → longitudinal. …

The Core Idea: How Particles Move vs. How the Wave Moves

The classification of a wave as transverse or longitudinal depends entirely on the direction of oscillation of the individual particles of the medium relative to the direction in which the wave energy travels.

• Transverse wave: Particles vibrate perpendicular (at right angles) to the wave's direction. Think of a wave on a string — the string moves up and down, but the wave moves left to right.
• Longitudinal wave: Particles vibrate parallel to the wave's direction. Think of sound in air — air molecules move back and forth along the same line the sound travels, creating compressions and rarefactions.
• Combination: The particle motion is more complex, often a circular or elliptical path, containing both perpendicular and parallel components relative to the wave direction. This is typical of surface water waves.

Let's apply this to each case.

Step-by-Step Analysis

1. (a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.

The spring itself is a medium that can support both types of waves. The key phrase is "displacing one end of the spring sideways." This means you give the end of the spring a perpendicular push relative to the spring's length.

This perpendicular displacement creates a kink that travels down the length of the spring. The coils of the spring move mainly sideways (perpendicular to the spring's axis) as the kink passes -- a transverse component. But because the coils are themselves elastically connected along the spring's length, the sideways kink also produces some bunching/stretching of the coils along the spring's own axis as it propagates -- a longitudinal component too. The real textbook's own printed answer to this example classifies this case as transverse and longitudinal (a combination), not purely transverse.

2. (b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.

The piston moves "back and forth" — that is, along the axis of the cylinder. This motion pushes and pulls on the liquid molecules directly in front of it.

The liquid molecules are forced to oscillate along the same line as the piston's motion. This creates alternating regions of high pressure (compression) and low pressure (rarefaction) that travel down the cylinder. The particle displacement is parallel to the wave's direction. This is a classic longitudinal wave.

3. (c) Waves produced by a motorboat sailing in water.

This refers to the surface waves created by the boat's hull moving through the water. Water molecules at the surface do not simply move up and down or back and forth. They move in an approximately circular (or elliptical) path. …

Step 1: Classify each wave by comparing the direction particles of the medium oscillate against the direction the disturbance travels: perpendicular = transverse, parallel = longitudinal, a mix (e.g. circular/elliptical particle paths) = combination.

Step 2 (a): Displacing the spring end sideways gives the coils a mainly perpendicular displacement, but the elastic coupling along the spring's length also carries some longitudinal disturbance as the kink travels — the real textbook's own printed answer classifies this as transverse and longitudinal (a combination), not purely transverse.

Step 3 (b): The piston moves back and forth along the cylinder's axis, pushing liquid molecules along that same line, creating travelling compressions/rarefactions — particle motion is parallel to propagation — longitudinal. …