Speed of Sound Calculator

Speed of sound in air depends primarily on temperature. Warmer air has faster-moving molecules, so sound travels faster. At 20°C it is 343 m/s; at 0°C it is 331 m/s.

🔊 Acoustics📐 v = √(γRT/M)🌡️ Temperature

Temperature T (°C)

Humidity (%) optional

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Speed in Air	v	v = 331.3√(T/273.15)	m/s
Temperature	T	In Kelvin	K
At 20°C	v	343 m/s	m/s
At 0°C	v	331 m/s	m/s
General Formula	v	√(γRT/M)	m/s

Step-by-Step Examples

Example 1

Room Temperature

Speed of sound at 20°C.

T = 20 + 273.15 = 293.15 K
v = 331.3 * sqrt(293.15/273.15)
v = 331.3 * 1.0365 = 343.2 m/s

✓ 343 m/s at 20°C

Example 2

Cold Day

-20°C winter conditions.

T = 253.15 K
v = 331.3 * sqrt(253.15/273.15) = 331.3 * 0.9631
v = 319.1 m/s

✓ 319 m/s — sound slower in cold air

Example 3

Body Temperature

At 37°C (inside lungs).

T = 310.15 K
v = 331.3 * sqrt(310.15/273.15) = 352.9 m/s

✓ 353 m/s at body temperature

Real-World Applications

🌴

Outdoor Acoustics

Temperature variations cause sound bending (refraction) and shadow zones in outdoor environments.

✈️

Aviation

Mach number = v_aircraft / v_sound. Sound speed varies with altitude and temperature.

📡

Sonar Systems

Sound speed in water (~1480 m/s) used for depth finding and submarine detection.

🎵

Concert Hall Design

Temperature variations in large halls affect sound delay and reverberation calculations.

Common Mistakes to Avoid

⚠️

Forgetting to convert to Kelvin

v = 331.3*sqrt(T/273.15) requires T in Kelvin. 20°C = 293.15 K, not 20 K.

⚠️

Ignoring humidity

Humid air is slightly less dense (water vapor is lighter than N2/O2), increasing sound speed by ~0.3% at 50% humidity.

⚠️

Assuming speed is constant

Speed changes significantly with temperature. A 30°C difference changes speed by about 11 m/s.

Frequently Asked Questions

Why does sound travel faster in hot air? ▾

Hotter air molecules move faster (higher kinetic energy). Sound propagates via molecular collisions, so faster molecules transmit pressure waves quicker.

How does altitude affect sound speed? ▾

Temperature drops ~6.5 K/km in troposphere. At 10 km (cruise altitude), T ~-50°C, sound speed ~299 m/s.

Why is Mach 1 not a fixed speed? ▾

Mach 1 equals the local speed of sound, which changes with temperature. At altitude (cold air), Mach 1 is slower than at sea level.

How fast does sound travel in water? ▾

~1480 m/s in fresh water (20°C), ~1520 m/s in sea water. Much faster than air due to higher bulk modulus.

What is acoustic impedance? ▾

Z = rho * v. Impedance mismatch between air and tissue reflects most sound — why ultrasound gel is needed in medical imaging.

Related Physics Calculators

Formula Explorer connections

Interpretation: This relationship connects frequency, wavelength, speed, phase, intensity or resonance in an oscillating system. Assumption: Identify the medium, boundary conditions and reference frame. Linear waves, small amplitudes, nondispersive media or ideal resonance may be assumed.

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