Utilities to calculate the speed of sound relative to temperature, humidity, and pressure.

sound_speed.py

"""
Original Code from: Dr Richard Lord - http://resource.npl.co.uk/acoustics/techguides/speedair/

Based on the approximate formula found in
Cramer, Owen. "The variation of the specific heat ratio and the speed of sound
in air with temperature, pressure, humidity, and CO2 concentration."
The Journal of the Acoustical Society of America 93.5 (1993): 2510-2516.

Saturation vapour pressure found in Richard S. Davis, "Equation for the
Determination of the Density of Moist Air (1981/91)", Metrologia,
29, p. 67-70, 1992,and a mole fraction of carbon dioxide of 0.0004.
The mole fraction is simply an expression of the number of moles
of a compound divided by the total number of moles of all the
compounds present in the gas.

I also used some info from http://www.sengpielaudio.com/calculator-airpressure.htm

"""

import math
import numpy as np

def log10(x):
    return math.log(x) / math.log(10)


def roundto(x, dp):
    return round(x * 10**dp) / 10**dp


def sqr(x):
    return x**2


def calculate_speed_of_sound(temperature, pressure, relative_humidity):
    # calculate speed of sound in humid air
    # only pressure 75 to 102
    # only temperature 0 to 30
    # only relative humidity 0 to 100
    # temperature in degrees Celsius
    # pressure in kilopascals
    # relative humidity in percent
    # returns speed of sound in meters per second
    # constants

    # Check that sensible numbers were entered
    if not (75 <= pressure <= 102):
        print("Pressure must be between 75 and 102 kPa")
        return 
    pressure_pa = pressure * 1000.0  # Convert to Pa

    # tested only for 0 to 40 degrees Celsius
    # if not (0 <= temperature <= 40):
    #     print("Temperature must be between 0 and 30 degrees Celsius")
    #     return
    # Check that sensible numbers were entered
    if relative_humidity > 100 or relative_humidity < 0:
        print("Relative humidity must be between 0 and 100%")
        return

    temperature_kelvin = 273.15 + temperature  # Measured ambient temp

    enhancement_factor = 3.141593 * 10**-8 * pressure_pa + 1.00062 + sqr(
        temperature) * 5.6 * 10**-7

    psv1 = sqr(temperature_kelvin
              ) * 1.2378847 * 10**-5 - 1.9121316 * 10**-2 * temperature_kelvin
    psv2 = 33.93711047 - 6.3431645 * 10**3 / temperature_kelvin
    psv = math.exp(psv1) * math.exp(psv2)

    water_vapor_concentration = relative_humidity * enhancement_factor * psv / pressure_pa
    mole_fraction_water_vapor = water_vapor_concentration / 100.0
    mole_fraction_carbon_dioxide = 400.0 * 10**-6

    c1 = 0.603055 * temperature + 331.5024 - sqr(
        temperature) * 5.28 * 10**-4 + (
            0.1495874 * temperature + 51.471935 -
            sqr(temperature) * 7.82 * 10**-4) * mole_fraction_water_vapor
    c2 = (-1.82 * 10**-7 + 3.73 * 10**-8 * temperature -
          sqr(temperature) * 2.93 * 10**-10) * pressure_pa + (
              -85.20931 - 0.228525 * temperature +
              sqr(temperature) * 5.91 * 10**-5) * mole_fraction_carbon_dioxide
    c3 = sqr(mole_fraction_water_vapor) * 2.835149 - sqr(
        pressure_pa
    ) * 2.15 * 10**-13 + sqr(
        mole_fraction_carbon_dioxide
    ) * 29.179762 + 4.86 * 10**-4 * mole_fraction_water_vapor * pressure_pa * mole_fraction_carbon_dioxide

    speed_of_sound = c1 + c2 - c3
    return speed_of_sound




# Call the function to calculate the speed of sound
tempreature, pressure, relative_humidity = 25, 101.325, 100
calculate_speed_of_sound(tempreature, pressure, relative_humidity)

# calculate average change in speed of sound per temperature change
def average_change_by_temp(pressure = 101.325, relative_humidity = 0):
    prev=0
     # kPa (standard pressure)
    relative_humidity = 0 # dry air
    total=[]
    for i in range(0,30):
        new=(calculate_speed_of_sound(i, pressure, relative_humidity))
        # print(new,new-prev)
        total.append((new-prev))
        prev=new

    print(sum(total[1:])/(len(total)-1))

# calculate average change in speed of sound per humidity change
def average_change_by_humidity(pressure = 101.325, temperature = 25):
    prev=0
     # kPa (standard pressure)
    temperature = 25 # dry air
    total=[]
    for i in range(0,100):
        new=(calculate_speed_of_sound(temperature, pressure, i))
        # print(new,new-prev)
        total.append((new-prev))
        prev=new

    print(sum(total[1:])/(len(total)-1))

print('Average change in speed of sound per degree Celsius')
print('(standard pressure), dry air')
average_change_by_temp(pressure = 101.325, relative_humidity = 0)
print('(standard pressure), wet air')
average_change_by_temp(pressure = 101.325, relative_humidity = 100)
print('low pressure, wet air')
average_change_by_temp(pressure = 75, relative_humidity = 100)
print('low pressure, dry air')
average_change_by_temp(pressure = 75, relative_humidity = 0)

print('\nAverage change in speed of sound per humidity')

average_change_by_humidity(pressure = 101.325, temperature = 25)
average_change_by_humidity(pressure = 101.325, temperature = 0)
average_change_by_humidity(pressure = 75, temperature = 25)
average_change_by_humidity(pressure = 75, temperature = 0)