Speed of Sound Calculator

Speed of Sound Guide

What do I need to know about Temperature and the Speed of Sound?

The speed of sound in air depends primarily on temperature: v = 331.3 × √(1 + T/273.15) m/s, where T is temperature in Celsius. At 0°C: 331 m/s. At 20°C: 343 m/s. At 100°C: 386 m/s. The relationship is not linear — it scales with the square root of absolute temperature. Humidity has a very small effect on speed of sound (less than 0.5% at typical conditions). Pressure changes (altitude) do not significantly affect the speed of sound at a given temperature — despite common misconception.

What should I know about Mach Numbers?

The Mach number is the ratio of an object's speed to the local speed of sound. Mach 1 = the speed of sound (approximately 343 m/s or 1,235 km/h at sea level and 20°C). Subsonic: below Mach 0.8. Transonic: Mach 0.8–1.2 (where shock waves begin to form). Supersonic: Mach 1–5. Hypersonic: Mach 5+. The speed of sound decreases with altitude as temperature falls — at 35,000 feet (typical cruise altitude), the speed of sound is approximately 295 m/s (Mach 1 at cruise = 1,062 km/h, compared to 1,235 km/h at sea level), meaning a fixed indicated airspeed corresponds to a higher Mach number at altitude than at ground level.

What do I need to know about Sound in Different Media?

Sound travels faster in denser, stiffer materials: air at 20°C (343 m/s) < water (1,481 m/s) < wood (3,500–4,200 m/s) < glass (5,640 m/s) < steel (5,960 m/s) < diamond (12,000 m/s). This is why knocking on a wall to detect a stud works — the denser wood produces a different acoustic response than the hollow cavity. Dolphins and whales exploit the higher speed of sound in water for long-distance communication — whale song can travel thousands of miles through ocean 'sound channels' where the speed of sound varies with depth, bending the sound path back toward a central layer instead of letting it disperse.

What should I know about Thunder and Sonic Booms?

Lightning produces a thunder clap at the strike location. The time between seeing lightning and hearing thunder tells you the distance: approximately 1km per 3 seconds (or 1 mile per 5 seconds). This works because light travels almost instantaneously at 300,000 km/s while sound travels at only 0.343 km/s. A sonic boom occurs when an aircraft or projectile exceeds the speed of sound — the shock wave produced is a cone trailing behind the object. The 'boom' is heard when this cone sweeps past a listener on the ground, which is why a sonic boom is heard as a single event even though the aircraft has been supersonic for some time beforehand.

What do I need to know about the Newton-Laplace Formula?

The speed of sound in a gas is given by the Newton-Laplace equation v = √(γP/ρ), where γ is the adiabatic index (ratio of specific heats, ≈ 1.4 for air), P is pressure, and ρ is density. Isaac Newton's original derivation assumed sound compresses air isothermally and under-predicted the speed by about 20%; Pierre-Simon Laplace corrected it in 1816 by recognising that sound compressions happen too fast for heat to escape, so they're adiabatic, not isothermal — adding the γ factor that brings the formula in line with the measured ~343 m/s at 20°C. The same style of formula, v = √(B/ρ), applies to liquids using the bulk modulus B.

What should I know about Humidity's Effect on the Speed of Sound?

Water vapour (molar mass ≈18 g/mol) is lighter than the nitrogen and oxygen molecules it displaces (28–32 g/mol), so humid air has a slightly lower average molecular mass and a marginally higher speed of sound than dry air at the same temperature — typically a fraction of a metre per second difference across the full humidity range. The effect is small compared to temperature's influence (about 0.6 m/s per °C) but is precise enough that professional acoustics and long-range artillery calculations still correct for relative humidity alongside temperature and pressure.

What should I know about Altitude and the Speed of Sound?

The speed of sound in air depends only on temperature, not on air pressure or density directly, but altitude still has a major practical effect because temperature itself falls as altitude increases. In the troposphere, the lowest layer of the atmosphere where most weather and aviation occurs, temperature drops at an average lapse rate of about 6.5°C per kilometre of altitude. Using the approximation that the speed of sound in air is roughly 331 + 0.6T m/s (with T in °C), a climb from sea level (around 15°C) to 10,000 metres (around −50°C) lowers the speed of sound from about 340 m/s to around 300 m/s — a reduction of over 10%. This matters enormously for aviation: an aircraft's Mach number depends on the local speed of sound, so the same physical airspeed corresponds to a higher Mach number at altitude than at sea level, which is why aircraft flying near their maximum safe Mach number must monitor altitude and temperature carefully. Weather balloons and atmospheric scientists use this same temperature-altitude relationship to map how sound and shock waves propagate differently through the atmosphere's layered temperature structure.

What should I know about the Speed of Sound at Different Air Temperatures?

Using v = 331.3√(1 + T/273.15), the speed of sound across a range of everyday air temperatures works out as follows:

Each 10°C step changes the speed of sound by roughly 6 m/s near room temperature, though the relationship is a square root, not a straight line, so the step size shrinks very slightly at higher temperatures and grows very slightly at lower ones.

What should I know about Using Echo Timing to Find Distance?

Speed of sound calculations are also used in echo ranging. Suppose a hiker shouts toward a canyon wall at an air temperature of 15°C and hears the echo return after 1.4 seconds. First find the local speed of sound: v = 331.3×√(1+15/273.15) = 331.3×√1.0549 = 331.3×1.0271 ≈ 340.3 m/s. Because the sound has to travel to the wall and back, the distance is half of speed × time, not the full value: distance = (340.3 × 1.4)/2 ≈ 238 metres. This same halving logic — travel time out and back, divide by two — underlies sonar depth-finding at sea and ultrasonic distance sensors in cars and robotics, all of which use a measured speed of sound (or speed of sound in water, roughly 1,481 m/s) and a round-trip timing measurement to calculate distance rather than measuring it directly.

What should I know about the Speed of Sound in Helium and Other Gases?

Changing the gas itself, not just its temperature, has a dramatic effect on the speed of sound — which is why inhaling helium famously (and briefly) raises the pitch of a person's voice. The full kinetic-theory formula for the speed of sound in an ideal gas is v = √(γRT/M), where γ is the gas's adiabatic index, R is the universal gas constant (8.314 J/(mol·K)), T is absolute temperature, and M is the gas's molar mass. Air (M ≈ 0.0290 kg/mol, γ ≈ 1.4) gives the familiar ~343 m/s at 20°C. Helium is both lighter (M ≈ 0.0040 kg/mol) and monatomic (γ ≈ 1.667), and plugging these into the same formula at 20°C (293.15K) gives v = √(1.667 × 8.314 × 293.15 / 0.0040) ≈ √1,015,700 ≈ 1,008 m/s — about three times faster than in air. Breathing helium doesn't change the vocal cords' actual vibration frequency, but it does raise the resonant frequencies of the vocal tract (which scale with the speed of sound in the gas filling it), shifting the perceived timbre upward into a cartoonish register even though the fundamental pitch is almost unchanged.

What should I know about the Doppler Effect and the Speed of Sound?

The speed of sound also governs the Doppler effect — the shift in a sound's perceived frequency when its source is moving relative to a listener. The observed frequency is f_obs = f_source × v/(v − v_source) as the source approaches (and v/(v+v_source) as it recedes), where v is the speed of sound and v_source is the source's speed. For a car horn at 500 Hz approaching a stationary listener at 30 m/s in 20°C air (v=343 m/s): f_obs = 500 × 343/(343−30) = 500×343/313 ≈ 548 Hz, a noticeably higher pitch, before dropping sharply to around 500×343/373 ≈ 460 Hz the instant it passes and recedes — the familiar 'pitch drop' heard as a fast vehicle or siren passes by.