The speed of sound wave is maximum in:

2019

The speed of sound wave is maximum in:

  1. A.

    Vacuum

  2. B.

    Water

  3. C.

    Air

  4. D.

    Steel

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Correct answer: D

The speed of a sound (mechanical) wave in a medium is governed by v = √(E/ρ), where E is the medium's elastic modulus (its resistance to deformation) and ρ is its density. A stiffer medium transmits vibrations from particle to particle faster, so wave speed is generally highest in solids, lower in liquids, and lowest in gases, while it is undefined in a vacuum, which has no particles at all.

Among the four options, steel is the only solid: its particles are rigidly bonded, giving it a very high elastic modulus that outweighs its higher density. Water is a liquid with weaker restoring forces between molecules than a solid has. Air is a gas whose widely spaced, weakly interacting molecules give it the smallest elastic modulus of the three media that actually carry sound. A vacuum has no medium at all, so no sound wave can propagate through it.

Medium

State of matter

Typical sound speed

Vacuum

No particles

No propagation

Water

Liquid

~1450-1500 m/s

Air

Gas

~340 m/s

Steel

Solid

~5000-6000 m/s

These typical measured values confirm the E/ρ reasoning above: rigidity dominates over density, so a rigid solid carries sound far faster than a liquid or gas, and a vacuum carries none at all. The speed of sound is therefore maximum in steel.

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