Speed of Sound Formula
Reference for v = 331.3 + 0.606T m/s speed of sound in air.
Calculate sound speed at any temperature and compare to water, steel, and other media.
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The Formula
v = 331.3 + 0.606 × T
The speed of sound in air depends on the temperature. Warmer air transmits sound faster because air molecules move more quickly at higher temperatures.
Variables
| Symbol | Meaning |
|---|---|
| v | Speed of sound in air (m/s) |
| T | Air temperature in degrees Celsius (°C) |
| 331.3 | Speed of sound at 0°C (m/s) |
| 0.606 | Speed increase per degree Celsius (m/s/°C) |
Example 1
Find the speed of sound at room temperature (20°C)
v = 331.3 + 0.606 × 20
v = 331.3 + 12.12
v = 343.4 m/s (about 1,236 km/h or 768 mph)
Example 2
Find the speed of sound at -15°C (cold winter day)
v = 331.3 + 0.606 × (-15)
v = 331.3 - 9.09
v = 322.2 m/s (about 1,160 km/h)
When to Use It
Use the speed of sound formula when:
- Calculating distances from thunder or echoes
- Designing concert halls and audio systems
- Computing Mach numbers for aircraft
- Adjusting sonar or radar calculations for temperature
Key Notes
- This formula applies to air only — sound travels ~1,480 m/s in water and ~5,100 m/s in steel, because denser elastic media transmit sound much faster
- Humidity has a small effect: moist air is slightly less dense than dry air at the same temperature, increasing sound speed by up to ~0.3% in very humid conditions
- The exact formula is v = 331.3 × √(T/273.15) where T is in Kelvin — the linear version above (v = 331.3 + 0.606T) is accurate to within 0.5% for everyday temperatures from −30°C to +50°C
Key Notes
- In air: v ≈ 331.3 + 0.606 × T(°C) m/s: Sound speed increases with temperature because warmer air molecules move faster. At 20°C: v ≈ 343 m/s; at 0°C: v ≈ 331 m/s. Humidity has a minor effect (moist air is slightly faster than dry air).
- General formula: v = √(γP/ρ) = √(γRT/M): γ ≈ 1.4 for diatomic gases (air), R is the gas constant, T is absolute temperature, and M is molar mass. Speed depends on the ratio of elasticity to inertia of the medium.
- Speed hierarchy: solids > liquids > gases: Solids have high bulk modulus (stiff) so sound travels fast despite higher density. Steel: ~5,100 m/s; water: ~1,480 m/s; air: ~343 m/s. This is why you hear a train through the tracks before through the air.
- Mach number and shock waves: At Mach 1 (object speed = sound speed), pressure waves pile up at the front — a shock wave forms. This causes a sudden pressure discontinuity heard as a sonic boom and a dramatic increase in aerodynamic drag.
- Applications: Sound speed is used in sonar (distance = speed × round-trip time / 2), ultrasound medical imaging, seismic wave analysis (earthquake locating), architectural acoustics (echo timing), thunder distance estimation (3 s per km), and speed-of-sound anemometers.