# Speed of Sound in Air as a Function of Temperature

• Paulene Gueco
In summary, the conversation discussed the topic of "Speed of Sound in Air as a Function of Temperature" and how to experimentally investigate it. Suggestions were made to set up a resonant air column and vary the air temperature, or use a whistle or an open pipe immersed in a water bath. The relationship between temperature and speed of sound in different fluids, such as air, water, and steel, was also mentioned. The possibility of a "sonic boom" in water was brought up and the conversation shifted to the mysterious loud booms underwater that do not match any known seismic signals. The potential for a shock wave in a fluid, such as water, was discussed.
Paulene Gueco
Hi, guys! :) I do hope I am posting on the right thread here.

So anyways, I'm looking into a certain topic: "Speed of Sound in Air as a Function of Temperature".

Any thoughts on how I could do this experimentally?

Warm regards,
Paulene :)

Set up a resonant air column and vary the air temperature to effect the resonant frequency.

Wow! I didn't expect to get an immediate reply. Thank you, Sir.

Would you be so kind to elaborate a little further as to how I may be able to set up an air column? :(

A whistle.

My Physics supervisor asked me to look into the topic for my Physics Extended Essay. I was thinking of maybe relating it with Airplanes and how they possibly break sound barriers? If that makes any sense?

Airplanes near the speed of sound are resistant to experiment.

Do you know the effect of temperature on the speed of sound in theory?

Awwww. So supposing I disregard that mentality and follow through with your suggested experiment, what research question could I formulate, Sir?

How does resonant frequency vary as temperature of air column? First do it qualitatively as you learn your equipment, heating causes rise or decline ins resonant. Acquire instruments for temperature and audio frequency and refine.

Oh, okay. Thank you very much, sir! I have a meeting with my Supervisor this Sunday and I have yet to find out what he thinks about it. If you've got any other suggestions, please let me know. It doesn't really have to be related to this topic, just something that's not too simple nor complex enough to do an experiment on.

Warm regards,
Paulene

And also, I've looked into the speed of sound with regards to the temperature. The lower the temperature is, the faster the travel of speed of sound.

Paulene Gueco said:
And also, I've looked into the speed of sound with regards to the temperature. The lower the temperature is, the faster the travel of speed of sound.

You made a mistake somewhere, then.

Wait, what?

The speed of sound in a gas that can be treated as a perfect gas (like air) has a well-known relationship with temperature, and it is not an inverse relationship.

hmmmmmmmmmmmmmmmmmmmm

Ohhh. That explains a lot. Thanks :)

Have you got suggestions on how I'd be able to do this experimentally as opposed to the one suggested above?

I mean, there are any number of ways depending on what equipment you have available and how accurate you need to be. You could even do something simple like put a sound source and a pressure transducer/microphone in a foam-lined box (for acoustic insulation) a known distance apart and then record how long it takes for the microphone to register a sound you tell the source to make.

If you have a source of audio tones and a microphone, you can find the resonant frequencies of an open pipe, immersed vertically in a water bath (to change the temperature).
If you look at the formula in this link , you can see that the change over the temperature range obtainable in a water bath is not great so you may need to be careful with your measurements.
Google 'Open Pipe Resonance' for the background knowledge. Hyper physics is your friend in this sort of problem.

The box brings up a story. Sonar location needs an accurate measure of the speed of sound in water that has more parameters than in air. So a box is used with an ultrasonic transmitter and receiver timing the travel of pulses through water continually sampled by an auxiliary system. Some numbers from that part of my life; speed of sound in air is about 1000 fps, in water about 5000 fps and in steel about 15000 fps - as I recall.

Doug Huffman said:
speed of sound in air is about 1000 fps, in water about 5000 fps and in steel about 15000 fps
That suddenly made me think of something that never crossed my mind before. If something could manage to go fast enough under water, would there be a "sonic boom" similar to what happens in air? If so, how would it propagate?
The main reason that I'm curious about it is because of the still-untraced massively loud "booms" from underwater (somewhere in or near Asia, I think) that don't match any other known seismic signals. Maybe a small but extraordinarily powerful sea-floor volcanic eruption could spit out a rock that fast?

Danger said:
would there be a "sonic boom" similar to what happens in air?
Very interesting thought! I don't think sound waves "pile up" in front of an object in water like they do in air. Perhaps they do, and if so it would seem to me the 1 to 5 ratio of the speed of sound in air vs. water would indicate the speed required would be mach 5! It seems like this might need its own thread...

jerromyjon said:
the speed required would be mach 5
That's not quite the right way to phrase it, since the definition of Mach 1 is the speed of sound in a fluid. So it would technically still be Mach 1 even if it's 5 times faster than the speed of sound in air (and that is dependent upon air density at the time). I know what you mean, though.

Oh thanks for the clarification, I've never even heard of mach in terms of fluid, but I do remember reading it varies with pressure/temperature.

Danger said:
That suddenly made me think of something that never crossed my mind before. If something could manage to go fast enough under water, would there be a "sonic boom" similar to what happens in air? If so, how would it propagate?
The main reason that I'm curious about it is because of the still-untraced massively loud "booms" from underwater (somewhere in or near Asia, I think) that don't match any other known seismic signals. Maybe a small but extraordinarily powerful sea-floor volcanic eruption could spit out a rock that fast?

There would definitely be a shock wave in a situation such as that. Water is not really that different from air in terms of forming shocks other than the much greater speed required to do so. Otherwise, it is mathematically the same, requiring only a different equation of state if I recall. I don't know how the sound associated with the shock structure would be perceived underwater, though. I suppose it may be sonic-boom-like.

jerromyjon said:
Oh thanks for the clarification, I've never even heard of mach in terms of fluid, but I do remember reading it varies with pressure/temperature.

Fluids are the primary context in which Mach number is used. Are you unclear about the difference between a fluid and a liquid (which is a type of fluid)?

Are you unclear about the difference between a fluid and a liquid (which is a type of fluid)?
A liquid is a fluid, same as air is a fluid in many respects.

Technically all matter is fluid from my understanding.

A fluid deforms, shears, to occupy the available shape volume. A gas is a fluid that expands.

@ Danger: There must be many man made projectiles that travel at >Mach 5. That's all you would need.

sophiecentaur said:
at >Mach 5.
My misunderstanding, mach 1 is the speed of sound in ANY given environment.

sophiecentaur said:
There must be many man made projectiles that travel at >Mach 5.
There are, but as far as I know they wouldn't have the "oomph" to make it through water at anything near that. As a much-slower example, a bullet from a .308 Winchester slows to the point that it won't injure someone within about 5 feet of entering water. I think that it's something like 8 feet for a .50 Barrett.
The only self-propelled things that I know of that can do Mach 5 are spacecraft , missiles, and some super-secret aeroplanes. None of those can even function under water, let alone overcome the extremely increased drag.

Last edited:
sophiecentaur said:
@ Danger: There must be many man made projectiles that travel at >Mach 5. That's all you would need.
Many individuals or categories?

The first generation of .17 (caliber) Remington rifle rounds were rated as 5050 fps but were de-rated in about ten years to 4000 fps for being too difficult to maintain. I brushed lead and gilding metal from my rifle's barrel each five rounds.

## 1. What is the speed of sound in air and how is it affected by temperature?

The speed of sound in air is the rate at which sound waves travel through the air. It is affected by temperature because sound waves travel faster in warmer air due to the increased speed of air molecules. As temperature increases, the molecules move faster and collide more frequently, allowing sound waves to travel faster.

## 2. How does the speed of sound change with increasing temperature?

As temperature increases, the speed of sound in air also increases. This is because the molecules in warmer air have more kinetic energy, allowing them to vibrate faster and transmit sound waves more quickly.

## 3. What is the relationship between temperature and the speed of sound in air?

The relationship between temperature and the speed of sound in air is directly proportional. This means that as temperature increases, the speed of sound also increases. Conversely, as temperature decreases, the speed of sound decreases.

## 4. How is the speed of sound in air measured and calculated?

The speed of sound in air can be measured using a device called a sound velocity meter, which sends out a sound wave and measures the time it takes for the wave to travel a known distance. It can also be calculated using the equation v = √(γRT), where v is the speed of sound, γ is the ratio of specific heats for air, R is the gas constant, and T is the temperature in Kelvin.

## 5. Why does the speed of sound in air change with temperature?

The speed of sound in air changes with temperature because temperature affects the density and elasticity of the air. As temperature increases, the air becomes less dense and more elastic, allowing sound waves to travel faster. Conversely, as temperature decreases, the air becomes more dense and less elastic, resulting in a slower speed of sound.

Replies
1
Views
3K
Replies
11
Views
2K
Replies
2
Views
2K
Replies
1
Views
799
Replies
11
Views
2K
Replies
4
Views
2K
Replies
6
Views
1K
Replies
5
Views
2K
Replies
4
Views
2K
Replies
29
Views
5K