How to Calculate Sonic Velocity
Sound travels through different gases at different speeds at different temperatures. You can calculate sonic, or sound, velocity easily enough with a simple formula based on the ideal gas law, a law that is accurate up to 150 PSI or 10 atmospheres. To use the formula, you only need a few physical constants for the medium through which the sound travels.
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Instructions
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Identify the medium’s adiabatic constant, also known as its heat capacity ratio. Calculate this yourself as the molar heat capacity at constant pressure divided by the molar heat capacity at constant volume. Or look up the adiabatic constant.<br /><br />For example, the adiabatic constant of air is ?=1.4, where ? is the Greek letter gamma.
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Convert the gas’s temperature, T, to the Kelvin scale. Start by converting Fahrenheit to Celsius by subtracting 32 and multiplying by 5/9. Convert Celsius to Kelvin by adding 273.
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Determine the molecular weight, M, of the gas in kilograms per mole. Dry air has an average molecular mass of 28.95 grams per mole. To find it for, say, hydrogen, look up the atomic weight of hydrogen gas. Most periodic tables give atomic weights of the elements. Hydrogen gas is diatomic, so you’d multiply the 1.0079 grams per mole by 2 to get 2.016 grams per mole of the molecule, or 0.002016 kg/mole.
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Calculate the sonic velocity using the formula ?[?RT/M]. Take the square root of the entire quantity in the brackets. Here, R is the universal gas constant, 8.314 Joules per mole Kelvin.<br /><br />For example, the speed of sound in air at 20 degrees Celsius comes out to ?[?RT/M] ?[1.4*8.314*293/0.02895] = 343.2 meters per second.
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