Speed of sound and the factors affecting it
Sound is fastest in solids, slower in liquids, slowest in gases. In a gas it rises with temperature and humidity and falls with density.
Speed of sound in different media (about 25 °C)
| Medium | State | Approximate speed |
|---|---|---|
| Air | Gas | About 346 m/s |
| Water | Liquid | About 1500 m/s |
| Iron or steel | Solid | About 5000 to 6000 m/s |
Why solids are fastest
Speed depends on how quickly one particle passes the push to the next. In a solid, particles are closely packed and strongly bound. A solid is also highly elastic: it springs back into shape quickly. So the disturbance passes very fast. In gases, particles are far apart and pass it on slowly. Sound is about four times faster in water than in air, and more than ten times faster in steel.
Factors affecting the speed of sound in a gas
| Factor | Effect | Rule or reason |
|---|---|---|
| Density (ρ) | Speed decreases as density increases | v ∝ 1/√ρ. Sound is 4 times faster in hydrogen than in oxygen, as oxygen is 16 times denser |
| Temperature | Speed increases with temperature | v ∝ √T (T in kelvin). In air, speed rises by about 0.61 m/s for each 1 °C rise |
| Relative humidity | Speed increases in humid air | Water vapour makes air less dense, so sound travels faster on a humid day |
| Pressure | No effect at constant temperature | Pressure and density change together, so their effects cancel |
Worked example: speed of sound on a hot day
The speed of sound in air at 0 °C is 331 m/s. Find its speed on a hot day in Chennai when the temperature is 35 °C.
- Formula: vT = v₀ + 0.61 T, where T is in °C.
- Given v₀ = 331 m/s, T = 35 °C.
- vT = 331 + (0.61 × 35) = 331 + 21.35.
- vT = 352.35 m/s ≈ 352 m/s (rounded to the nearest whole number).
About 352 m/s
Worked example: how far is the lightning?
During a monsoon storm, you hear thunder 3 s after you see the lightning flash. The speed of sound in air is 340 m/s. How far away is the lightning?
- Light reaches you almost at once, so the 3 s delay is the time taken by the sound.
- Formula: distance = speed × time.
- d = 340 m/s × 3 s = 1020 m.
1020 m, about 1 km
At Diwali, you see a rocket burst in the sky before you hear its bang, because light is far faster than sound. In the monsoon, count the seconds between lightning and thunder to judge how far away the storm is.
2 marks: “Why does sound travel faster in solids than in gases?” The particles of a solid are closely packed and the solid is highly elastic, so the vibration passes from particle to particle faster.
4 marks: “Explain how density, temperature and humidity affect the speed of sound in a gas.” Higher density: lower speed (v ∝ 1/√ρ). Higher temperature: higher speed (about 0.61 m/s per °C). Higher humidity: lower density, so higher speed.
4 marks: “The speed of sound in air at 0 °C is 331 m/s. Find its speed at 20 °C.” vT = v₀ + 0.61 T = 331 + 0.61 × 20 = 331 + 12.2 = 343.2 m/s.
Solids are Speediest; Hot and Humid air is faster; Dense gas Drags sound.