Speed of Sound in a Medium Calculator
Enter the medium's elastic modulus and density to find the speed of sound.
Result
How it is calculated
The speed of a sound wave in a fluid or solid is v = √(K ÷ ρ), where K is the elastic (bulk) modulus in pascals (Pa) and ρ is the density in kg/m³. The result is in metres per second. The tool also converts it: km/h is v × 3.6, mph is v × 2.23694, and the Mach figure is v ÷ 343, so Mach here is relative to the speed of sound in air at 343 m/s, not to the medium itself. Both inputs must be above zero. Enter the modulus in Pa, not GPa: a value like 2.2e9 or 2200000000 is accepted. For a thin solid rod, use Young's modulus as K; for a liquid or a gas, use the bulk modulus. The formula does not include temperature, so enter the modulus and density that apply at your temperature.
Worked example
Fresh water has a bulk modulus of about 2.2 × 109 Pa, written 2200000000, and a density of 1000 kg/m³. Divide: 2,200,000,000 ÷ 1000 = 2,200,000. Take the square root: √2,200,000 = 1,483.24 m/s. In other units: × 3.6 = 5,339.66 km/h, × 2.23694 = 3,317.91 mph. Relative to air at 343 m/s, that is 1,483.24 ÷ 343 = 4.324, shown as the Mach figure.
Common mistakes
- Entering the modulus in GPa or MPa. The field is in pascals, so typing 2.2 for 2.2 GPa gives about 0.05 m/s instead of 1,483 m/s. Convert to Pa first.
- Entering the density in g/cm³. It must be kg/m³: water is 1000, not 1.
- Using Young's modulus for a liquid or gas, or the bulk modulus for a thin rod. Pick the modulus that matches how the wave moves in your medium.
- Reading the Mach figure as relative to the medium. It is always divided by 343 m/s, the speed of sound in air.
- Ignoring temperature. The modulus and density change with it, and so does the speed; use values for the temperature you care about.
About this calculator
The speed of sound in a medium depends on how stiff and how dense that material is: v = √(K/ρ), where K is the elastic (bulk) modulus and ρ is the density. Stiffer materials transmit pressure disturbances faster because their particles snap back into place more quickly, which is why sound travels only about 343 m/s in air but roughly 1,480 m/s in water and around 5,000–6,000 m/s in steel — despite steel being far denser, its bulk modulus is proportionally even higher.
This same relationship (using Young's modulus E instead of K for a thin solid rod) is the basis for ultrasonic thickness testing, sonar depth-finding, and seismic surveying, where the travel time of a sound or shock wave reveals properties of the material it passed through. Acoustic and materials engineers, geophysicists doing seismic surveys, and non-destructive testing technicians use this formula to predict sound speed in a new material or to work backward from a measured speed to infer a material's stiffness or density.
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