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Full Version: (15C) Speed of Sound in Air
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Formula used:

The speed of sound in air can be approximated by:
c ≈ √( γ * R * T / M)

where:

R = molar gas constant = 8.314 4625 618 153 J/(K * mol)
R = 8.314 4625 618 153 (kg * m^2)/(s^2 * K * mol)

M = molar mass of air = 0.02897 kg/mol

γ = adiabatic index of air = 1.4


C ≈ 20.04503702 * √T ≈ 331.2893427 * √((°C + 273.15) / 273.15)


Instructions:

To calculate the speed of sound when the temperature is in Fahrenheit (°F), press [ f ] { A } or [ GSB ] { A } [ R/S ].

To calculate the speed of sound when the temperature is in Celsius (°C), press [ f ] { B } or [ GSB ] { B } [ R/S ].

To calculate the speed of sound when the temperature is in Kevin (K), press [ f ] { C } or [ GSB ] { C } [ R/S ].

Code:
Code:

Step ; Key Code ; Key
001 ; 42, 21, 11 ; LBL A
002 ; 3 ; 3
003 ; 2 ; 2
004 ; 30 ; -
005 ; 5 ; 5
006 ; 20 ; ×
007 ; 9 ; 9
008 ; 10 ; ÷
009 ; 42, 22, 12 ; LBL B
010 ; 2 ; 2
011 ; 7 ; 7
012 ; 3 ; 3
013 ; 48 ; .
014 ; 1 ; 1
015 ; 5 ; 5
016 ; 40 ; +
017 ; 42, 22, 13 ; LBL C
018 ; 11 ; √
019 ; 2 ; 2
020 ; 0 ; 0
021 ; 48 ; .
022 ; 0 ; 0
023 ; 4 ; 4
024 ; 5 ; 5
025 ; 0 ; 0
026 ; 3 ; 3
027 ; 7 ; 7
028 ; 0 ; 0
029 ; 2 ; 2
030 ; 20 ; ×
031 ; 36 ; ENTER
032 ; 36 ; ENTER
033 ; 2 ; 2
034 ; 48 ; .
035 ; 2 ; 2
036 ; 3 ; 3
037 ; 6 ; 6
038 ; 9 ; 9
039 ; 3 ; 3
040 ; 6 ; 6
041 ; 20 ; ×
042 ; 34 ; X<>Y
043 ; 43, 32 ; RTN


Examples:

68 °F: 68 [ f ] { A } -> 343.20358 m/s, 767.72445 mph
35 °C: 35 [ f ] { B } -> 351.87462 m/s, 787.83024 mph
280 K: 280 [ f ] { C } -> 335.41762 m/s, 750.30776 mph

Source

“Speed of Sound” Wikipedia. Last Edited March 27, 2024. https://en.wikipedia.org/wiki/Speed_of_sound Retrieved April 7, 2024
With the above formulae and data, and applying 1st order Taylor development (to get rid of the square root), you get this easy to remember formulae, and very simple to apply without a calculator:

c[m/s] about 331.3 + 0.61×T[in Celsius] or
c[m/s] about 331+ 0.6×T[in Celsius].

For Fahrenheit
c[m/s] about 320.6+ 1/3×T[in Fahrenheit] or
c[m/s] about 321+T/3[in Fahrenheit].

Gil
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