# The Speed of Sound (in gases)

The speed of sound is the velocity at which sound travels through a medium, which can be a solid, liquid or a gas.
The following calculations, however, only relate to the speed of sound through a gas - any gas.

The conventional calculation method for the speed of sound is as follows:
v = √[γ.Rᵢ.Ṯ / RAM]
Where: γ is normally rounded off to 1.4
However, this calculation method only considers temperature as a variable. It takes no account of gas density or pressure.

CalQlata has established a more accurate value for our atmosphere; γ = cₚ/cᵥ = 965.4/719.3 = 1.34213819
When both options for 'γ' are applied to the above formula and a column of Earth's atmosphere, the following velocities are achieved:

γ = 1.4 γ = 1.342
Altitude (km) Ṯₑ (K) Ṯₚ (K) vₑ (m/s) vₚ (m/s) vₑ (m/s) vₚ (m/s)
0353.15293.15374.41341.13366.59334
5321.9261.9357.46322.43350315.7
10290.65230.65339.67302.58332.58296.27
15278.15218.15332.28294.27325.34288.13
20278.15218.15332.28294.27325.34288.13
25285.65225.65336.73299.29329.7293.04
30293.15233.15341.13304.22334297.87
35303.15243.15346.9310.68339.65304.19
40313.15253.15352.57317345.21310.38
45323.15263.15358.16323.2350.68316.45
50333.15273.15363.66329.28356.06322.41
55323.51263.51358.36323.42350.87316.67
60307.44247.44349.34313.4342.05306.86
65291.36231.36340.08303.05332.98296.72
70275.29215.29330.57292.34323.67286.23
75259.22199.22320.78281.21314.08275.34
80243.15183.15310.68269.63304.19264
85243.15183.15310.68269.63304.19264
90243.15183.15310.68269.63304.19264
95248.15188.15313.85273.29307.3267.58
100253.15193.15317276.9310.38271.11
The velocity of sound using the formula; v = √[γ.Rᵢ.Ṯ / RAM]
suffix 'ₚ' refers to the earth's polar atmosphere, and suffix 'ₑ' refers to the earth's equatorial atmosphere

If, on the other hand, we apply the following formula:
v = √[γ.p / ρ]
Where: p is the pressure and ρ is the density at altitude, both of which include the effects of temperature and centrifugal force, we achieve the following velocities (assuming γ = 1.34213819):

γ = 1.342
Altitude (km) pₑ (N/m²) pₚ (N/m²) ρₑ (kg/m³) ρₚ (kg/m³) vₑ (m/s) vₚ (m/s)
0101118.51102439.981.021.24364.77333.46
566585.1567454.577.35E-019.09E-01348.68315.57
1039908.3640429.004.87E-016.17E-01331.68296.46
1522646.6522941.842.88E-013.70E-01324.71288.53
2013281.6213454.591.69E-012.16E-01325.05288.83
258068.078173.049.96E-021.27E-01329.78294.09
304843.874906.855.82E-027.37E-02334.16299.00
352915.252953.123.39E-024.25E-02339.66305.21
401936.721961.862.18E-022.71E-02345.46311.64
451216.991232.771.33E-021.64E-02350.94317.74
50799.09809.458.45E-031.04E-02356.23323.64
55517.81524.515.64E-036.97E-03350.99317.83
60312.99317.033.59E-034.49E-03342.05307.89
65190.69193.162.31E-032.92E-03333.02297.74
70113.20114.661.45E-031.87E-03323.68287.19
7563.3664.188.63E-041.13E-03313.99276.18
8033.9634.394.93E-046.59E-04304.04264.75
8517.9218.152.60E-043.48E-04303.94264.67
909.449.561.37E-041.83E-04303.84264.57
955.165.227.35E-059.75E-05306.84268.07
1002.983.024.16E-055.49E-05309.85271.55
The velocity of sound using the formula; v = √[γ.p / ρ]
suffix 'ₚ' refers to the earth's polar atmosphere, and suffix 'ₑ' refers to the earth's equatorial atmosphere

As you can see, the differences are marginal:

Altitude (km)vₑ/vₑvₚ/vₚ
00.9950458380.99839082
50.9962356010.999584906
100.9972940571.000642774
150.9980614721.001380355
200.9990953011.002415099
251.0002508031.003584712
301.0004730711.00380485
351.0000170931.003350699
401.0007241251.004074591
451.000729541.004084586
501.0004754751.003803713
551.0003415491.003662682
601.0000138531.003353763
651.0001128441.003446124
701.0000317171.003369555
750.9997134381.00304549
800.9995067921.002843592
850.9991927491.002525425
900.9988351721.002163978
950.9985131881.00183269
1000.998288511.001609543
A comparison of the two calculation methods
suffix 'ₚ' refers to the earth's polar atmosphere, and suffix 'ₑ' refers to the earth's equatorial atmosphere

Given the closeness of the two calculation methods, either can be considered appropriate for general use.
However, it is CalQlata's opinion, that v = √[γ.p / ρ] is the most reliable formula as it takes into account the pressure and density of the gas, which if calculated correctly, will never give reason to doubt the accuracy of your calculation result, irrespective of gas composition and conditions. It may, however, require a little more work, dependent upon the information available.