# Speed of Sound Calculator

The Java source code of this applet and its documentation are freely available.

Notes:

• A programa calculates speed of sound for a temperature range of 0 to 30 degrees C and relative humidity 0 to 100% RH.

• The algorithm is based on the approximate formula published in JASA  by Owen Cramer, "The variation of the specific heat ratio and the speed of sound in air with temperature, pressure, humidity, and CO2 concentration."

f (t, p, xw, xc) = a0 + a1 t + a2 t2 + (a3 + a4 t + a5 t2) xw + (a6 + a7 t + a8 t2) p + (a9 +a10 t +a11 t2) xc + a12 xw2 + a13  p2 + a14 xc2 + a15 xw p xc
where the t is the celsius temperature, p is the pressure, xw is the water vapor mole fraction, and xc is the carbon dioxide mole fraction.
The coefficients are:
a0 = 331.5024
a1 = 0.603 055
a2 = -0.000 528
a3 = 51.471 935
a4 = 0.149 587 4
a5 = -0.000 782
a6 = -1.82 * 10-7
a7 = 3.73 * 10-8
a8 = -2.93 * 10-10
a9 = -85.209 31
a10 = -0.228 525
a11 = 5.91 * 10-5
a12 = -2.835 149
a13 = -2.15 * 10-13
a14 = 29.179 762
a15 = 0.000 486

xw = h f psv / p
where h is the relative humidity expressed as a fraction, f is the enhancement factor, and psv is the saturation vapor pressure of water vapor in air.

f = 1.000 62 + 3.14 * 10-8 p + 5.6 * 10-7 t2

and

psv = exp (1.281 180 5 * 10-5 T2 - 1.950 987 4 * 10-2 T + 34.049 260 34 - 6.353 631 1 * 103 / T) Pa

The above equations are only valid over the temperature range 0 C to 30 C.

• Reference: J.Acoust.Soc.Am.93(5) p2510-2616; formula at p2514.