Speed of Sound Calculator
Free speed of sound calculator — speed in air by temperature plus water, steel and other media, with Mach number and distance from an echo delay.
Free speed of sound calculator — speed in air by temperature plus water, steel and other media, with Mach number and distance from an echo delay.
In air, v ≈ 331.3 + 0.606 T with temperature in Celsius. Pressure does not appear, which is why sound travels at nearly the same speed at sea level and on a mountain at the same temperature — altitude matters only because it is colder up there.
Count the seconds after the flash and multiply. Three seconds to a kilometre, five to a mile — and if it is under thirty, go indoors.
Speakers 34 metres from the stage need about 100 ms of delay to stay in sync. Get it wrong and the audience hears everything twice.
Clap facing a wall, time the return, halve it. A surprisingly accurate way to measure across a valley or a large hall.
Colder air means slower sound, so an aircraft can be flying slower and be nearer the sound barrier. Instruments show Mach for exactly this reason.
Sound moves nearly three times faster in helium, which shifts the resonances of your vocal tract upward. Your vocal cords are unchanged.
Both time an echo through a known medium. Getting the speed right for tissue or seawater is what turns a delay into a depth or an image.
About 343 metres per second at 20 °C, which is 1,235 km/h or 767 mph. The useful approximation is v = 331.3 + 0.606 T with the temperature in Celsius, accurate to well under one percent across ordinary conditions. At freezing point it drops to about 331 m/s and on a hot 35 °C day it rises to roughly 352 m/s — a difference large enough to matter for outdoor sound systems and for anything timing an echo.
Pressure has essentially no effect on its own, which surprises most people. Sound speed in an ideal gas depends on temperature and on the gas itself, not on pressure, because a change in pressure alters density and stiffness in ways that cancel. Altitude matters only indirectly: the air is colder higher up, and that is what slows sound down. Humidity has a small effect, raising the speed by well under one percent in very humid air.
Because sound moves faster in stiffer materials. It travels at roughly 1,481 m/s in fresh water — more than four times its speed in air — and about 5,960 m/s in steel, some seventeen times faster. Density pulls the other way, which is why very dense but soft materials such as rubber carry sound remarkably slowly, around 60 m/s. Stiffness relative to density is what sets the speed.
Count the seconds between the flash and the thunder and multiply by the speed of sound. Light arrives effectively instantly, so the delay is almost entirely sound travel time. Three seconds means roughly one kilometre; five seconds means about a mile. The same arithmetic works for an echo, except that the sound makes a round trip, so you halve the result to get the distance to the reflecting surface.
Mach number is an object's speed divided by the local speed of sound, so Mach 1 is exactly sonic. Because the speed of sound falls with temperature, the same true airspeed is a higher Mach number at altitude where the air is colder — an aircraft can be flying more slowly and be closer to the sound barrier. That is why aircraft instruments display Mach rather than airspeed alone at high altitude, since the aerodynamic behaviour depends on the ratio and not the raw speed.