# sound_speed_units.py (Source)

```"""
Compute the "equilibrium" and "frozen" sound speeds for a gas. Uses the pint library to
include customized units in the calculation.

Requires: Cantera >= 3.0.0, pint
Keywords: thermodynamics, equilibrium, units
"""

import cantera.with_units as ctu
import numpy as np

# This sets the default output format of the units to have 2 significant digits
# and the units are printed with a Unicode font. See:
ctu.units.default_format = ".2F~P"

def equilibrium_sound_speeds(gas, rtol=1.0e-6, max_iter=5000):
"""
Returns a tuple containing the equilibrium and frozen sound speeds for a
gas with an equilibrium composition.  The gas is first set to an
equilibrium state at the temperature and pressure of the gas, since
otherwise the equilibrium sound speed is not defined.
"""

# set the gas to equilibrium at its current T and P
gas.equilibrate('TP', rtol=rtol, max_iter=max_iter)

# save properties
s0 = gas.s
p0 = gas.P
r0 = gas.density

# perturb the pressure
p1 = p0*1.0001

# set the gas to a state with the same entropy and composition but
# the perturbed pressure
gas.SP = s0, p1

# frozen sound speed
afrozen = np.sqrt((p1 - p0)/(gas.density - r0)).to("ft/s")

# now equilibrate the gas holding S and P constant
gas.equilibrate('SP', rtol=rtol, max_iter=max_iter)

# equilibrium sound speed
aequil = np.sqrt((p1 - p0)/(gas.density - r0)).to("ft/s")

# check against the built-in sound speed function
afrozen2 = gas.sound_speed.to("ft/s")

return aequil, afrozen, afrozen2

# test program
if __name__ == "__main__":
gas = ctu.Solution('gri30.yaml')
gas.X = 'CH4:1.00, O2:2.0, N2:7.52'
T_range = np.linspace(80, 4880, 25) * ctu.units.degF
print("Temperature      Equilibrium Sound Speed     Frozen Sound Speed      Frozen Sound Speed Check")
for T in T_range:
gas.TP = T, 1.0 * ctu.units.atm
print(T.to("degF"), *equilibrium_sound_speeds(gas), sep = "               ")
```