Which of the following statements are true for wave motion? (a) Mechanical transverse waves can propagate thro

NCERT Exemplar · Q6

Q. Which of the following statements are true for wave motion?

(a) Mechanical transverse waves can propagate through all mediums.

(b) Longitudinal waves can propagate through solids only.

(d) Longitudinal waves can propagate through vacuum.

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Concept understanding — Wave Type Classification

Wave Type Classification: From Intuition to Precision

Imagine you're standing at the edge of a still pond. You drop a pebble. Ripples spread outward in circles. Now imagine you're holding one end of a long rope tied to a wall. You flick your wrist once — a single hump travels down the rope, hits the wall, and comes back. These are both waves, but they behave differently. Why?

The key difference lies in what is moving versus what is waving.

The Core Intuition

A wave is a disturbance that carries energy from one place to another without permanently moving the medium itself. But the direction of that disturbance relative to the wave's travel direction gives us our first major classification.

Think of a crowd at a stadium doing "the wave." People stand up and sit down (the disturbance moves up-down), but the wave itself travels around the stadium (left-right). The motion of each person is perpendicular to the wave's travel. That's one type.

Now think of a slinky stretched on a table. If you push one end toward the other, a compression travels along the slinky. Each coil moves along the same line as the wave — forward and back. That's the other type.

The Precise Classification

Waves are classified into two fundamental types based on the relationship between the direction of particle displacement (how the medium moves) and the direction of wave propagation (which way the energy travels).

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Transverse Waves

In a transverse wave, the particles of the medium oscillate perpendicular to the direction the wave travels.

Example: Light waves (electromagnetic waves), waves on a string, water waves (surface component), seismic S-waves
Key feature: The wave has crests (high points) and troughs (low points)
Visual: Think of a rope shaken up and down — the rope moves vertically, the wave moves horizontally

Longitudinal Waves

In a longitudinal wave, the particles of the medium oscillate parallel to the direction the wave travels.

Example: Sound waves in air, seismic P-waves, slinky compressions
Key feature: The wave has compressions (regions of high density) and rarefactions (regions of low density)
Visual: Think of a slinky pushed and pulled — coils bunch up and spread out along the same line the wave moves

Note

Some waves are neither purely transverse nor purely longitudinal. Water waves, for instance, have particles moving in circular paths — a combination of both. These are called surface waves or Rayleigh waves in seismology.

Why This Matters

This classification isn't just academic. It determines:

What materials a wave can travel through: Transverse waves (like light) can travel through vacuum. Longitudinal waves (like sound) need a medium. But mechanical transverse waves (like rope waves) also need a medium — the distinction is about how the medium moves, not whether a medium exists. …

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Wave motion is classified by the medium's response (transverse vs. longitudinal) and the need for a medium (mechanical vs. non-mechanical). Mechanical waves require a material medium; transverse mechanical waves need shear elasticity (solids only), while longitudinal waves need bulk elasticity (solids, liquids, gases). Vacuum supports no mechanical waves. The only true statement is (C).

Why This Approach Works

The question tests two independent classifications of waves: transverse vs. longitudinal (based on particle displacement relative to wave direction) and mechanical vs. non-mechanical (based on whether a material medium is required). A mechanical wave must have a medium that provides the restoring force. For transverse waves, that restoring force comes from shear elasticity — the ability of the medium to resist a sideways deformation. For longitudinal waves, it comes from bulk elasticity (compression/rarefaction). Solids have both; liquids and gases have only bulk elasticity. Vacuum has none. So the truth of each statement follows directly from these physical properties.

Statement (A): "Mechanical transverse waves can propagate through all mediums."

This is false. Transverse mechanical waves require a medium that resists shear — that is, a solid. Liquids and gases cannot sustain a shear stress; if you try to push a layer of water sideways, it simply flows. So they cannot support transverse mechanical waves. (Electromagnetic waves are transverse but non-mechanical — they don't need a medium at all.)
Statement (B): "Longitudinal waves can propagate through solids only."

This is false. Longitudinal (compressional) waves rely on bulk modulus — the resistance to volume change. Solids, liquids, and gases all have a bulk modulus (though gases have a very small one). Sound in air is a longitudinal wave; sound in water is a longitudinal wave. So longitudinal waves propagate through all three states of matter.
Statement (C): "Mechanical transverse waves can propagate through solids only."

This is true. As argued above, only solids possess the shear modulus needed to transmit a transverse mechanical disturbance. Liquids and gases lack shear elasticity, so they cannot carry such waves.
Statement (D): "Longitudinal waves can propagate through vacuum." …

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Q.Which of the following statements are true for wave motion?

Why This Approach Works

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