Why sound is faster on a warm day

Sound doesn't have one fixed speed. In air at 0 °C it travels about 331 metres a second. On a 20 °C day it's about 343. Every degree warmer adds roughly 0.6 m/s. That's not much, but if you measure distances with sound, it adds up.

A push passed along

Sound is a squeeze passed from molecule to molecule. A speaker pushes the air next to it, those molecules bump into the next ones, and the push travels on. Air molecules are always zipping about, and the warmer the air, the faster they go. So they hand the push along sooner.

The rule behind it is neat: the speed goes with the square root of the absolute temperature, which counts up from absolute zero, −273.15 °C. On that scale, going from 0 °C to 20 °C is only about 7% warmer, so sound gets about 3.6% faster.

The speeds are for dry air, from 331.3 × √(1 + T/273.15) m/s with T in °C. The echo times (ms means thousandths of a second) are for the trip there and back.

What hardly matters

Pressure, surprisingly, makes no difference, as long as the temperature stays the same. Squeeze air and it gets springier, but it also gets denser by the same amount, and the two cancel out. So the thin air up a mountain isn't slower in itself. What counts is how warm it is.

Humidity matters a little. Water vapour is lighter than the rest of the air, so damp air is slightly faster. Even completely saturated air at 20 °C is only about 0.4% faster than dry air. That's about 1.3 m/s, or what two degrees of warming would do. (At 30 °C it's about 0.7%.)

Why a ruler cares

A ruler made of sound doesn't measure distance. It measures time, then multiplies by the speed of sound. Use the wrong speed, and every reading is off by the same share. One degree is worth about 0.17%. Ten degrees is about 1.7%: some 3.4 cm on a 2 m reading.

Sound that bends at night

Because sound is faster in warm air, it bends when the temperature changes with height. On a still night the ground cools off, and the air near it can end up colder than the air above. The top of a sound wave, up in the warmer air, runs ahead of the bottom, so the wave turns back down toward the ground. That's why you can often hear things from farther away at night.

Taking the ocean's temperature

Sound in water speeds up in the warmth too, and by more: about 4 to 5 m/s for every degree in seawater. Scientists have used that to take the temperature of whole oceans.

In January 1991, for the Heard Island Feasibility Test, a ship near Heard Island in the southern Indian Ocean lowered underwater loudspeakers into the sea. Listeners at 16 sites around the world waited for their coded, low hum. The day before the official start, the team ran a five-minute check of the sound sources. About three and a half hours later, a listener in Bermuda reported hearing it, and soon after came word from Whidbey Island, near Seattle. Both were about 18,000 km away, nearly halfway around the Earth.

The idea: over a long path, warmer water makes the trip a little quicker. So timing the same trip again and again shows whether the ocean in between is warming. A decade of that followed, from 1996 to 2006, in the North Pacific: the Acoustic Thermometry of Ocean Climate project.

Try it with Sonar Ruler

This is why Sonar Ruler asks for the temperature. Every distance it shows is a time multiplied by the speed of sound, and the speed comes from the temperature you set. Its wheel runs from −10 to 45 °C (14 to 113 °F), and it shows the speed that goes with each degree: 343.2 m/s at 20 °C, from the same formula as the table above.

1. Open Two Phones on two phones (both need the app). Lay them about 2 m apart with their bottom edges facing, and wait for STEADY.
2. Tap the temperature pill and roll the wheel. The phones still hear the same timing, but now it's worth a different distance: the reading moves about 3.4 cm for every 10 degrees.
3. Save one reading at your room's real temperature and one at 0 °C. History keeps each with its temperature and the speed of sound that went with it.

Sources

• Smithsonian National Air and Space Museum, How Things Fly: How does the speed of sound in air vary with temperature?
• NASA Glenn Research Center, Speed of Sound
• D. Bohn, Environmental Effects on the Speed of Sound, Journal of the Audio Engineering Society 36(4), 1988
• COMSOL Blog, Why Sounds Travel Farther at Night
• W. Munk, R. Spindel, A. Baggeroer and T. Birdsall, The Heard Island Feasibility Test, Journal of the Acoustical Society of America 96(4), 1994
• The Heard Island Feasibility Test (project site)