Maths⏱ 4 min read
How to Calculate the Speed of Sound in Different Media
The speed of sound is not fixed — it varies with temperature, medium, and pressure. Here is the formula for air, water, and solids, plus the maths behind Mach numbers.
Sound travels as a pressure wave through a medium. Its speed depends on how quickly that medium can transmit the disturbance — which is why sound moves faster in water than air, and faster in steel than water.
Speed of Sound in Air
v = 331.3 x sqrt(1 + T/273.15) m/s
where T is temperature in Celsius
Or simplified:
v ≈ 331.3 + (0.606 x T) m/s (accurate within 0.1% for -20 to 50°C)
At standard conditions (20°C):
v = 331.3 + (0.606 x 20) = 331.3 + 12.12 = 343.4 m/s ≈ 343 m/s
At 0°C: v = 331.3 m/s
At -20°C: v = 331.3 + (0.606 x -20) = 319.2 m/s
At 40°C: v = 331.3 + 24.24 = 355.5 m/s
Key: sound travels faster in warmer air (molecules move more energetically)
Humidity has a very small effect — negligible for most purposes.
Speed of Sound in Other Media
MediumSpeed (m/s)vs Air (20°C)
Air at 20°C3431x (reference)
Water at 20°C1,4804.3x faster
Seawater at 20°C1,5304.5x faster
Concrete3,100-3,700~10x faster
Glass5,100-5,700~16x faster
Steel5,96017.4x faster
Diamond12,00035x faster
Mach Number
Mach number = Object speed / Local speed of sound
(Local = speed of sound in the medium at that location/temperature)
An aircraft flying at 700 km/h (194.4 m/s) at 20°C:
Mach = 194.4 / 343 = 0.567 (Mach 0.567)
Mach 1 = speed of sound (sonic)
Below Mach 1 = subsonic
Mach 0.8-1.2 = transonic
Mach 1.2-5.0 = supersonic
Above Mach 5 = hypersonic
At 10,000m altitude (temperature ~-50°C):
Speed of sound: 331.3 + (0.606 x -50) = 301 m/s
Concorde's cruising speed (2,140 km/h = 594 m/s):
Mach = 594 / 301 = 1.97 (approximately Mach 2)
Distance Estimation (Thunder Timing)
Time between lightning flash and thunder x 343 m/s = distance
3 seconds: 3 x 343 = 1,029m ≈ 1 km away
10 seconds: 10 x 343 = 3,430m ≈ 3.4 km away
Rule of thumb: divide seconds by 3 for km (or by 5 for miles)
"30/30 rule" for lightning safety:
If thunder within 30 seconds of lightning: seek shelter immediately
(means storm is within ~10km)
Wait 30 minutes after last thunder before resuming outdoor activity