Why is speed of sound constant?

[Curl]

This just occurred to me a few minutes ago, sorry if it's a dumb question:'

Why is the speed of sound constant in an ideal gas?

Suppose you have a box with an ideal mono atomic gas and a diaphragm that can oscillate. The diaphragm busts one move at ~3000 m/s. Since collisions with ideal gas particles are modeled elastically, the RMS speed of the particles that were in contact with the diaphragm while moving is ~3000m/s. Consequently, the neighboring particles will be bumped to ~3000m/s also, and so on until the end of the box is reached. Since no energy is lost and the RMS speed in the other two dimensions is zero, won't the pressure wave be traveling at ~3000m/s?

 

[AJ Bentley]

The analysis is a little more complex.

http://www.grc.nasa.gov/WWW/K-12/airplane/snddrv.html"

 

[cortiver]

By the way, the speed of sound is of the same order as the RMS speed of molecules in the gas, but the original RMS speed of molecules due to thermal motion is going to be much greater than the speed at which the diaphragm is moving.

 

[zguzel46]

thank you (teşekkür ederim)

 

[PJC01]

I can understand your curiosity about the constant speed of sound in an ideal gas. It is not a dumb question at all, and in fact, it is a very interesting one. The speed of sound in an ideal gas is indeed constant, and this is due to the properties of an ideal gas and the interactions between its particles.

Firstly, in an ideal gas, the particles are assumed to be point masses with no volume and no intermolecular forces, meaning they do not attract or repel each other. This allows for easy calculations and simplifies the understanding of gas behavior. In this type of gas, the speed of sound is determined by the average speed of the particles, which is directly related to the temperature of the gas. This means that as long as the temperature remains constant, the speed of sound will also remain constant.

Additionally, the speed of sound in an ideal gas is also affected by the density of the gas. In an ideal gas, the density is directly proportional to the pressure and inversely proportional to the temperature. This means that as the pressure increases, the density increases, and thus, the speed of sound also increases. However, the temperature remains constant, so the speed of sound remains constant as well.

Furthermore, in an ideal gas, the particles move in a straight line until they collide with another particle or the walls of the container. These collisions are perfectly elastic, meaning that no energy is lost during the collision. This is why the speed of sound remains constant as the pressure wave travels through the gas. The particles continue to transfer energy to each other, maintaining the constant speed of sound.

In conclusion, the constant speed of sound in an ideal gas is a result of the properties of an ideal gas and the interactions between its particles. The average speed of the particles, the density of the gas, and the elastic collisions all contribute to the constant speed of sound. I hope this explanation helps to answer your question.