Speed of Sound- temperature dependent

[Texas97]

i posted this was on the other site in OSR and i remembered i wanted to bring this over here.



just a reminder, for those shooting suppressed 22lr and looking to cut out the sonic crack, the speed of sound varies with temperature. this is the only thing that causes a variation in the speed of sound, and atmospheric pressure has no bearing on it.


i had to remind myself about this as i was shooting at the ranch on Saturday and it was roughly 37 degrees outside, and i was getting sonic crack with bulk pack through my 4.5" barrel AR with a can. so what was happening was the speed of sound in the colder air is much slower, and therefore a bullet velocity of a 22lr advertised at 1260 FPS on the box, out of a 4.5" barrel was still breaking the sound barrier.

for those wondering, here are a few equations and a refresher on calculating speed of sound.

we'll use U.S. Customary Units.

Ss = sqrt[k gc R T]

Ss= speed of sound
k= specific heat of air = 1.4
gc= gravity = 32.2 ft-lbm/(lbf-sec^2)
R= specific gas constant for air
T= absolute temperature in Rankine= degrees in F plus 460 (or 459.67 to be exact)


1st, calculate the specific gas constant:

R= R* / MW

R* = universal gas constant in Rankine units = 1545.4 ft-lbf/lbmol-Rankine
MW = molecular weight of air = 28.967 lbm/lbmol

R= 1545.4 / 28.967 = 53.35 ft-lbf/lbm-Rankine

Temperature at my shooting time: 37 deg F = 497 Rankine


Therefore:


Ss = sgrt[ (1.4)(32.2)(53.35)(497)]

Speed of sound on Saturday was = 1093.3 FPS




so to simplify this down, to calculate speed of sound for a given temperature (x in Fahrenheit), use this equation:

Ss = sgrt[ (1.4)(32.2)(53.35) (x+460)]


obviously, these equations treat air as an ideal gas.


applying this to my situation leads to the conclusion that the 4.5" barrel was not able to slow a 22lr bullet down from an advertised 1260 FPS to below 1093 FPS.

just food for thought.

 

[Roc Doc]

The sound engineers in the know, know that a PA tuned during soundcheck, will sound different once all the blood bags come in and the temp goes up. Of course humans in clothing absorb sound, but the temp changes have just as much of an effect.

 

[surpip]

the speed of sound varies with temperature. this is the only thing that causes a variation in the speed of sound, and atmospheric pressure has no bearing on it.

Really?
So the speed of sound being different at sea level and at 30k feet is only due to temperature change??

 

[Texas97]

Really?
So the speed of sound being different at sea level and at 30k feet is only due to temperature change??

thats correct. but dont take my word for it. this link gives a very layman's answer. i used to have the math worked out where it showed that air pressure falls out of the equation and is therefore not a component. but i think that was 10 years ago.

| How Things Fly

No. The speed of sound in air depends only on the temperature of the gas. Sound is a vibration that spreads as a wave through particles, such as those in air. Temperature is a measure of how energetic those particles are, hence, how fast they are moving. The more energetic the air particles are...

howthingsfly.si.edu

ASK AN EXPLAINER​

Q:

Does sound velocity depend on pressure?​

A:
No. The speed of sound in air depends only on the temperature of the gas. Sound is a vibration that spreads as a wave through particles, such as those in air. Temperature is a measure of how energetic those particles are, hence, how fast they are moving. The more energetic the air particles are, the faster sound waves travel through the air. If the pressure of the air around you were to double, but the temperature remained the same, the speed of sound would stay the same.

 

[surpip]

thats correct. but dont take my word for it. this link gives a very layman's answer. i used to have the math worked out where it showed that air pressure falls out of the equation and is therefore not a component. but i think that was 10 years ago.

That's pretty cool, I guess I never really looked into it.
Seems like humidity would affect it as well no?

 

[Texas97]

That's pretty cool, I guess I never really looked into it.
Seems like humidity would affect it as well no?

only to the affect that humidity has on temperature.

i had always heard all these claims about pressure and humidity and elevation above sea level and its only temperature that effects the speed of sound.

but i think people get confused between what affects the speed of sound and atmospheric conditions that affect external ballistics, bullet flight paths, wind drift, etc.

 

[surpip]

only to the affect that humidity has on temperature.

But sound moves faster in water so it would make sense to me the the humidity would affect it as well, since that would change the density of the air.

 

[Texas97]

But sound moves faster in water so it would make sense to me the the humidity would affect it as well, since that would change the density of the air.

apples to oranges. Humidity in the air is still a gas. sound traveling through a liquid plays by another set of rules. to build off the air particles touched on in the link, it probably has something to do with the molar volume of air vs water.

1 mol of water=18 mililiters

1 mol of air = 24 liters

so, therefore, there is a LOT more water molecules in any given volume than there are in air. which would lend itself to why sound waves travel through those particles 4-5 times faster. sound needs particles to travel through.

which is why there is no sound in a vacuum or in space.