For mechanical waves such as sound in ordinary materials, the speed of sound is maximum in which of the following states of matter?

Introduction / Context:
Sound is a mechanical wave, which means it requires a material medium such as air, water or solids to travel. The speed at which sound travels depends strongly on the properties of the medium, including its elasticity and density. Knowing where sound travels fastest is a standard concept in physics and helps explain phenomena such as hearing underwater, seismic wave propagation and ultrasonic testing of metals. This question asks you to identify the state of matter in which the speed of sound is maximum among the given options.

Given Data / Assumptions:

• Sound requires a material medium and cannot propagate in vacuum.
• In general, solids have particles that are closely packed and strongly bonded.
• Liquids have particles less tightly bound than solids but closer than in gases.
• Gases have particles far apart with weak intermolecular forces.

Concept / Approach:
The speed of sound in a medium depends on the ratio of the medium elastic properties to its density. In simple terms, sound travels faster in materials where particles can quickly transmit compressions and rarefactions. Solids usually have very strong elastic forces between particles and relatively modest densities compared to those forces, so the speed of sound is highest in solids. In liquids, the speed is lower than in solids but higher than in gases. In gases like air, the particles are far apart and the restoring forces are weaker, so sound travels slowest. In vacuum, there is no matter to carry the wave, so sound cannot travel at all and its speed is effectively zero.

Step-by-Step Solution:
Step 1: Recall the general rule: v_solid > v_liquid > v_gas for the speed of sound in typical materials.Step 2: Recognise that solids such as steel or rock have tightly packed particles that quickly pass on vibrations.Step 3: Understand that liquids like water have less tightly bound particles, so sound travels fast but not as fast as in solids.Step 4: Note that gases like air have loosely spaced particles, resulting in the lowest speeds among the three states of matter.Step 5: Remember that sound cannot travel in vacuum at all, because there are no particles to vibrate.Step 6: Conclude that the speed of sound is maximum in solids.

Verification / Alternative check:
Typical numerical values confirm this trend. At room temperature, the speed of sound in air is about 340 m/s, in water it is roughly 1500 m/s and in steel it can be about 5000 m/s or more. These values clearly show that sound travels fastest in solid materials. Seismologists use the high speed of seismic waves in rock to study Earth interior, and engineers use ultrasonic waves in metals for non destructive testing, both relying on the fact that sound speeds are high in solids.

Why Other Options Are Wrong:
Gases such as air have the lowest sound speed among the three common states of matter, so they cannot be the state where sound is fastest. Liquids allow sound to travel faster than in gases but still slower than in solids. Vacuum does not support sound propagation at all, as sound waves require a material medium. Therefore, none of these options except solids can represent the state where the speed of sound is maximum.

Common Pitfalls:
Students sometimes mistakenly think that sound should travel fastest in gases because sound is commonly associated with air. Others may think that because light travels fastest in vacuum, sound must do the same, forgetting that light is an electromagnetic wave while sound is mechanical. To avoid these mistakes, keep in mind that sound needs matter to travel and that the closer and more strongly bound the particles are, the faster sound can move through the material.

Final Answer:
The speed of sound is maximum in solids such as steel or rock.