Boneyard Tools

How temperature changes the speed of sound

Why warm air carries sound faster, the dry-air formula behind it, and how a shifting speed of sound moves the wavelength of a fixed note.

Open the Sound Wavelength Calculator →

Sound is a pressure wave in a medium

Sound travels as a wave of compression and rarefaction passing through a medium such as air, not as moving material carried along with it. How fast that disturbance propagates depends on how quickly the medium springs back when squeezed, which is set by its stiffness and its density. In a gas like air, warming it up makes the molecules move faster and transmit the pressure change more readily. That is the physical reason the speed of sound rises with temperature rather than with the loudness or pitch of the sound.

The dry-air formula

For dry air a compact approximation is used: the speed equals 331.3 times the square root of (1 + temperature in Celsius divided by 273.15) metres per second. The 331.3 figure is the speed at 0 C, and the 273.15 converts Celsius to the absolute Kelvin scale. Plugging in 20 C gives about 343.21 m/s, the familiar room-temperature value. The relationship is close to a straight line near everyday temperatures, gaining roughly 0.6 m/s for every degree Celsius, so a cold winter room and a hot summer one differ by a few metres per second.

How the wavelength follows

Wavelength is speed divided by frequency, so for a fixed note the wavelength scales with whatever speed of sound applies. A 440 Hz tone sits near 0.78 metres at 20 C, but in colder air where sound travels slower the same note has a slightly shorter wavelength, and in warmer air a slightly longer one. The period, by contrast, is just 1 divided by the frequency and does not move with temperature at all. That split is worth remembering: temperature bends the spatial size of a wave while leaving its timing untouched.

Where it matters in practice

Wind instruments drift in pitch as they warm up because the speed of sound inside the bore rises, changing the resonant frequencies of a fixed tube length. Outdoors, temperature layers bend sound paths, which is why distant noise can carry unusually far on a cool evening. In room acoustics the wavelength at a problem frequency tells you the scale of treatment needed, and using the right temperature keeps that estimate honest. When conditions are unusual, entering a measured speed directly avoids relying on the dry-air assumption.

Frequently asked questions

Roughly how much does the speed of sound change per degree?

Near room temperature it changes by about 0.6 metres per second for each degree Celsius. So a 10 degree swing shifts the speed by roughly 6 m/s, enough to nudge the wavelength of a fixed note.

Does a higher speed of sound change the pitch I hear?

Not for a sound source of fixed frequency; the pitch stays the same and only the wavelength changes. For resonant instruments, though, a changed speed of sound alters which frequencies resonate, which is heard as a pitch shift.

Should I use temperature mode or set the speed directly?

Use temperature mode for ordinary air where you know the temperature. Switch to setting the speed directly for other media like water, for humid or high-altitude conditions, or when you have a measured value.