Previous in Forum: Pressing multiple buttons on a touch panel Next in Forum: Appropriate Flow meter to measure Diesel for generator
Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63

# Speed of sound

01/03/2022 5:29 AM

Does anybody know of a formula to calculate the speed of sound in gases without the use of the isentropic exponent [or adiabatic constant]?

Interested in this topic? By joining CR4 you can "subscribe" to

Check out these comments that don't yet have enough votes to be "official" good answers and, if you agree with them, rate them!
Guru

Join Date: Aug 2007
Posts: 22636
#1

### Re: Speed of sound

01/03/2022 7:24 AM

__________________
“ When people get what they want, they are often surprised when they get what they deserve " - James Wood
Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63
#6

### Re: Speed of sound

01/04/2022 6:49 AM

Thank you for your comment. I was primarily looking for a formula where I could input the data.

2
Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9046
#2

### Re: Speed of sound

01/03/2022 8:13 AM

$c\,&space;=\,&space;\sqrt{\gamma&space;\times&space;\frac{P}{\rho&space;}}$

Where

P = pressure

ρ = density

γ = Ratio of specific heat.

https://byjus.com/speed-of-sound-formula/

The ratio of specific heat can be calculated from the number of degrees of freedom, the number of modes the gas molecule can vibrate.

https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry)

"Relation with degrees of freedom

The heat capacity ratio (γ) for an ideal gas can be related to the degrees of freedom (f) of a molecule by

Degrees of freedom of gases with one or N atoms

Monatomic

Linear molecules

Non-linear molecules

Translation (

x, y, and z)

333
Rotation (

x, y, and z)

023

Total (disregarding Vibration at room temperatures)

356
Vibration0(3

N − 5)

(3

N − 6)

Total (including Vibration)

3

6N-5

6N-6

https://en.wikipedia.org/wiki/Heat_capacity_ratio

Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63
#7

### Re: Speed of sound

01/04/2022 6:50 AM

Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9046
#11

### Re: Speed of sound

01/05/2022 11:33 AM

Sound is a traveling compression wave. A gas increases temperature when compressed. The γ factor arises because this compression is so rapid that heat doesn't have enough time to escape, and thus the compression is adiabatic (no heat transfer) rather than isothermal (no temperature change). Early calculations of sound speed in air did not take this into account.

is the adiabatic index also known as the isentropic expansion factor. It is the ratio of the specific heat of a gas at constant pressure to that of a gas at constant volume (Cp/Cv) and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression;"

https://en.wikipedia.org/wiki/Speed_of_sound

The connection between γ and degrees of freedom, f, is described here, and has to do with the equipartition of added energy (heat) to the gas as is done with a passing sound wave.

https://thefactfactor.com/facts/pure_science/physics/degree-of-freedom-of-gas-molecules-specific-heat/7594/

Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63
#12

### Re: Speed of sound

01/06/2022 5:07 AM

Thank you for taking the trouble to give me such a detailed answer. My initial hope was to have a simple formula for the speed of sound, without the isentropic exponent. I use the isentropic in other calculations, but found that it was difficult to calculate one without having the other. I did find a formula for the isentropic by Moshfeghian [via Science Direct] but believe that is for single gases. In ISO/DIS 20765-5 there is another calculation which involves both temperature and pressure, so I will see how that compares with know results.

Again, thank you for your replies.

Guru

Join Date: Jan 2007
Location: In the bothy, 7 chains down the line from Dodman's Lane level crossing, in the nation formerly known as Great Britain. Kettle's on.
Posts: 30310
#3

### Re: Speed of sound

01/03/2022 10:18 AM

...or one might simply look it up.

__________________
"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63
#8

### Re: Speed of sound

01/04/2022 6:52 AM

Thank you. However, I am looking for various gases.

Guru

Join Date: Jan 2007
Location: In the bothy, 7 chains down the line from Dodman's Lane level crossing, in the nation formerly known as Great Britain. Kettle's on.
Posts: 30310
#9

### Re: Speed of sound

01/05/2022 3:00 AM

Please evaluate whether withholding that information from the forum is actually helpful in progressing towards a satisfactory answer.

__________________
"Did you get my e-mail?" - "The biggest problem in communication is the illusion that it has taken place" - George Bernard Shaw, 1856
Commentator

Join Date: Sep 2009
Location: Adjacent to the brick fields in Beds
Posts: 63
#10

### Re: Speed of sound

01/05/2022 5:18 AM

I am confused at your comment. What information do you imagine I am withholding from the forum? My answer to you was merely that I was looking at gases - nothing more.

Anonymous Poster #1
#4

### Re: Speed of sound

01/03/2022 11:16 AM

v=√γRT/M

Use Ideal 7/5 gas in this situation, whatever that is???

try air, Air is 1.4

2
Guru

Join Date: Apr 2010
Location: About 4000 miles from the center of the earth (+/-100 mi)
Posts: 9046
#5

### Re: Speed of sound

01/03/2022 10:21 PM

Air is about 99% N2 and O2, which are 2 atom gases. Two atom molecules have three degrees of translational freedom and two degrees of rotational freedom for a total of five.

f = 5.

γ = 1+2/f = 1+2/5 = 1.4

Interested in this topic? By joining CR4 you can "subscribe" to