What is the formula for the speed of sound in a gas?

The exact formula is v = sqrt(gamma times R times T divided by M), where gamma is the ratio of specific heats, R = 8.314 J/(mol.K), T is temperature in Kelvin, and M is molar mass in kg/mol. For dry air, this simplifies to approximately v = 20.05 times sqrt(T_K) m/s.

Why does sound travel faster in solids than in air?

In solids, molecules are tightly bound with strong intermolecular forces (high bulk modulus), so pressure disturbances propagate very quickly. Air molecules are weakly coupled, so the same disturbance travels much more slowly. Steel transmits sound at about 5960 m/s, roughly 17 times faster than air.

What is the speed of sound at altitude?

In the troposphere, temperature decreases at about 6.5°C per km of altitude. At cruising altitude (11 km), temperature is roughly -56°C, giving v approximately 295 m/s (1062 km/h). A Mach 0.85 commercial jet at this altitude travels at about 251 m/s = 903 km/h, which is why your ground speed can be near 900 km/h while the aircraft is subsonic.

Is the speed of sound constant?

No. The speed of sound depends on the medium, temperature, pressure (for ideal gases, it is independent of pressure but depends on temperature), and composition. In dry air, it varies from about 299 m/s at -50°C to 386 m/s at 100°C. In liquids and solids it also varies with temperature and for solids with the direction of propagation relative to crystal axes.

How do I convert the speed of sound to Mach number for a vehicle?

Mach number = vehicle speed / local speed of sound. At 20°C at sea level, Mach 1 = 343.2 m/s. A car travelling 30 m/s (108 km/h) is at Mach 0.087. A bullet at 900 m/s is Mach 2.6. Use the Gas mode to find the local speed of sound first, then divide your vehicle speed by that value.

Speed of Sound Calculator

Q: What is the speed of sound in air at 20 degrees C?

The speed of sound in dry air at 20°C is 343.2 m/s (1235 km/h or 767 mph). This is Mach 1 at standard room temperature. It is the most commonly cited value for everyday reference.

Q: How does temperature affect the speed of sound?

Speed of sound increases with temperature. The relationship is: v is proportional to the square root of temperature (in Kelvin). In air, a useful linear approximation is v approximately equals 331 plus 0.6 times T_Celsius m/s. At 0°C, v = 331 m/s; at 20°C, v = 343 m/s; at 40°C, v = 355 m/s.

Q: What is the speed of sound in water?

The speed of sound in fresh water at 20°C is about 1481 m/s, and in seawater (salinity 35 ppt) at 20°C it is about 1521 m/s. Water temperature raises the speed by roughly 4 m/s per degree Celsius, and salinity adds about 1.4 m/s per ppt.

Q: What is Mach 1 in km/h and mph?

Mach 1 at sea level (15°C ISA standard day) is approximately 340.3 m/s = 1225 km/h = 761 mph. At 20°C it is 343.2 m/s = 1235 km/h = 767 mph. The value changes with altitude and temperature.

Q: Why does helium change the pitch of your voice?

Sound travels about 3 times faster in helium than in air because helium is about 7 times lighter (lower molar mass). The resonant frequencies of your vocal tract scale with the speed of sound in the surrounding gas, so they shift to about 3 times higher, producing the characteristic squeaky pitch.

Compute speed of sound in any gas at any temperature, or look up reference values for liquids and solids.

Gas

Temperature20°C

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-50°C100°C

Medium

Speed of Sound

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km/h

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mph

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Knots

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Temperature (K)

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Formula

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Speed of Sound

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km/h

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mph

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vs Air at 20°C

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Wavelength at 1 kHz

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🔊 What is the Speed of Sound Calculator?

The speed of sound calculator computes how fast a pressure wave (sound) propagates through a given medium. In a gas such as air, the speed depends primarily on temperature and the molecular properties of the gas. In liquids and solids it depends on density and the elastic modulus of the material. This calculator covers both cases: a temperature-based gas mode using the exact thermodynamic formula, and a reference table for common liquids and solids.

Practical applications include: aviation (Mach number is defined as vehicle speed divided by local speed of sound, which changes with altitude and temperature), acoustics engineering (room reverberation and speaker placement depend on the local speed of sound), underwater sonar (the 1481 m/s value for fresh water determines sonar pulse timing), medical ultrasound (soft tissue at 1540 m/s is the calibration standard for diagnostic imaging), and non-destructive testing of materials (measuring ultrasonic pulse speed reveals cracks and voids in metals and concrete).

A common misconception is that Mach 1 is a fixed speed. It is not. Mach 1 equals the local speed of sound, which is about 340 m/s at sea level on a standard day but only about 295 m/s at 11 km altitude where it is much colder. Supersonic aircraft must compute their Mach number using the local atmospheric temperature, not a fixed reference.

The calculator uses the ideal gas formula v = sqrt(gamma x R x T / M), where the inputs are the ratio of specific heats (gamma), the universal gas constant R = 8.314 J/(mol.K), temperature T in Kelvin, and molar mass M in kg/mol. For dry air at 20°C this gives 343.2 m/s, matching standard reference values to 4 significant figures.

📐 Formula

v = √(γ × R × T ÷ M)

v = speed of sound (m/s)

γ = ratio of specific heats (1.40 for dry air, 1.667 for noble gases)

R = universal gas constant = 8.31446 J/(mol·K)

T = absolute temperature (Kelvin) = T_Celsius + 273.15

M = molar mass of gas (kg/mol); dry air = 0.028964 kg/mol

Example: Dry air at 20°C: v = √(1.40 × 8.314 × 293.15 / 0.028964) = 343.2 m/s

Linear approx (air only): v ≈ 331 + 0.6 × T_C m/s (within 0.5% for 0 to 40°C)

📖 How to Use This Calculator

Steps

Choose Gas or Media mode - Select Gas to compute the speed in any gas at a given temperature, or Media to look up preset values for water, metals, concrete, and biological tissue.

Set your inputs - For Gas mode: pick the gas from the dropdown and drag the temperature slider or type a value in Celsius. For Media mode: select the material from the list.

Read all unit conversions - The results panel shows the speed in m/s, km/h, mph, and knots, plus temperature in Kelvin for gas mode, or a comparison to air and wavelength at 1 kHz for media mode.

💡 Example Calculations

Example 1 — Standard Room Temperature (Dry Air, 20°C)

What is the speed of sound in dry air at room temperature (20°C)?

Gas: Dry Air (gamma = 1.400, M = 0.028964 kg/mol). Temperature: 20°C = 293.15 K.

v = sqrt(1.400 x 8.314 x 293.15 / 0.028964) = sqrt(117,837) = 343.2 m/s.

Converting: 343.2 m/s = 1235.5 km/h = 767.3 mph = 667.0 knots. This is Mach 1 at standard room temperature.

Speed of sound = 343.2 m/s (1235.5 km/h)

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Example 2 — Speed of Sound in Helium (Why Does Your Voice Change?)

Speed of sound in helium at 20°C (explains the voice-pitch effect)

Gas: Helium (gamma = 1.667, M = 0.004003 kg/mol). Temperature: 20°C = 293.15 K.

v = sqrt(1.667 x 8.314 x 293.15 / 0.004003) = sqrt(1,018,553) = 1009 m/s.

Helium is 1009 / 343.2 = 2.94 times faster than air. Vocal resonant frequencies scale with sound speed, so your voice pitch rises to roughly 3 times its normal frequency when your vocal tract is filled with helium.

Speed in He = 1009 m/s (2.9x faster than air)

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Example 3 — Speed of Sound in Steel

How fast does sound travel in structural steel?

Steel longitudinal wave speed: 5960 m/s (from elastic modulus E = 200 GPa, density 7850 kg/m3).

Compared to air at 20°C: 5960 / 343.2 = 17.4 times faster.

Wavelength at 1 kHz = 5960 / 1000 = 5.96 m. This is why ultrasonic testing of steel uses MHz frequencies to achieve millimetre-scale defect resolution.

Speed in steel = 5960 m/s (17.4x faster than air)

Try this example →

❓ Frequently Asked Questions

What is the speed of sound in air at 20 degrees Celsius?+

At 20°C, the speed of sound in dry air is 343.2 m/s (1235.5 km/h or 767.3 mph). This is the standard Mach 1 reference at room temperature. The ISA sea-level standard day (15°C) gives 340.3 m/s = 1225 km/h = 761 mph.

What is the formula for speed of sound in a gas?+

The exact formula is v = sqrt(gamma x R x T / M), where gamma is the adiabatic index (1.4 for diatomic gases like air), R = 8.314 J/(mol.K) is the universal gas constant, T is temperature in Kelvin, and M is the molar mass in kg/mol. For air, this simplifies to v = 20.05 x sqrt(T_K) m/s.

How does temperature affect the speed of sound in air?+

Speed of sound increases with temperature because hotter molecules move faster and transmit pressure disturbances more quickly. The linear approximation v = 331 + 0.6 x T_C m/s is accurate to within 0.5% for everyday temperatures. At 0°C: 331 m/s; 20°C: 343 m/s; 40°C: 355 m/s.

What is the speed of sound in water?+

The speed of sound in fresh water at 20°C is about 1481 m/s. In seawater (salinity 35 ppt) at 20°C it is about 1521 m/s. Water is about 4.3 times denser than air but far more elastic, making sound travel about 4.3 times faster. Temperature raises the value by roughly 4 m/s per degree Celsius.

What is Mach 1 in km/h at sea level?+

At ISA sea-level standard conditions (15°C, 101,325 Pa), Mach 1 = 340.3 m/s = 1225 km/h = 761 mph. At 20°C it is 343.2 m/s = 1235 km/h = 767 mph. At cruising altitude (-56°C), Mach 1 drops to about 295 m/s = 1062 km/h.

Why does sound travel faster in steel than in air?+

Speed of sound in a material equals sqrt(elastic modulus / density). Steel has an enormous elastic modulus (200 GPa) that far outweighs its higher density, giving v = 5960 m/s. Air's low elastic modulus (142 kPa bulk modulus) produces only 343 m/s. The ratio is about 17 to 1.

Why does helium change the pitch of your voice?+

Sound travels about 2.9 times faster in helium than in air at the same temperature (1009 vs 343 m/s), because helium is about 7 times lighter. Resonant frequencies of your vocal tract scale directly with the speed of sound in the surrounding gas, so all resonant peaks shift up by a factor of about 2.9, producing the characteristic high-pitched sound.

Does air pressure affect the speed of sound?+

For an ideal gas, pressure cancels out in the formula (since density is proportional to pressure at constant temperature), so the speed of sound in an ideal gas depends only on temperature, not pressure. In practice, real-gas effects at very high pressures cause a small deviation, but for normal atmospheric conditions this is negligible.

What is the speed of sound in human tissue?+

The average speed of sound in human soft tissue is about 1540 m/s. This is the standard assumption used in diagnostic ultrasound equipment. Bone is faster (about 3000 m/s) and lung tissue is much slower (about 650 m/s) due to trapped air. The 1540 m/s calibration constant affects depth measurements in ultrasound imaging.

How do I calculate Mach number for a moving vehicle?+

Mach number = vehicle speed / local speed of sound. Use the Gas mode to find the speed of sound at the relevant temperature and altitude. For example, at 10 km altitude (about -50°C), v = 299 m/s. A jet at 800 km/h (222 m/s) is at Mach 0.74. The same jet at sea level (20°C, v = 343 m/s) is at Mach 0.65.

What is the wavelength of sound at 1 kHz in air?+

Wavelength = speed / frequency. At 20°C, v = 343 m/s, so wavelength at 1 kHz = 343 / 1000 = 0.343 m (34.3 cm). At 20 kHz (upper hearing limit): 343 / 20000 = 0.017 m (1.7 cm). In steel at 1 kHz: 5960 / 1000 = 5.96 m. This is why ultrasonic testing uses MHz frequencies to achieve millimetre resolution in solids.

What is the speed of sound in CO2 compared to air?+

Carbon dioxide (CO2) has a molar mass of 44 g/mol vs 29 g/mol for air, making it heavier. Combined with a lower gamma (1.289 vs 1.40), the speed of sound in CO2 at 20°C is about 267 m/s, compared to 343 m/s in dry air. CO2 is therefore a denser acoustic medium and sound travels about 22% slower in it.

🔗 Related Calculators

📌 Quick Tips

💡At 20°C (68°F) in dry air, the speed of sound is 343.2 m/s (1235 km/h). This is the standard Mach 1 reference for aviation.

💡Sound travels roughly 4.3 times faster in water than in air, and up to 17 times faster in steel. This is why underwater explosions can be heard from great distances.

💡The linear approximation v = 331 + 0.6 x T_C gives results within 0.5% for typical atmospheric temperatures (0 to 40°C).

💡Helium is much lighter than air, so sound travels about 3 times faster in it. This is why breathing helium raises the pitch of your voice.

💡In cold air at -50°C (typical upper atmosphere), Mach 1 is only about 299 m/s. Supersonic aircraft speeds are defined relative to the local speed of sound, not sea-level Mach 1.