Unraveling the Mystery of the Speed of Sound

[flycast]

I posted a question at another forum about "choked flow" where a fluid (in this case air) if flowing through a very small orifice. Apparently when the pressure difference on each side of a orifice is about 2:1 and above then the speed of the air passing through the orifice is limited to the speed of sound. This got me thinking...what is so special about the speed of sound?

Please, I am a non physicist. I know that the speed of sound varies depending on the density of air and humidity, etc. but it is fairly constant. I also know that the speed of sound is much faster but fairly constant in water. Increasing the energy makes for louder sound but not faster sound.

Why is the speed of sound fairly constant within the same medium? What keeps it from slowing down or speeding up significantly? What is the principal that limits sound to a fairly narrow speed?

 

[negitron]

The speed of sound is nothing more than the speed at which pressure differentials can propagate through a given medium. Sound happens to be pressure waves we can hear, but the limit applies to all pressure differentials. It's why planes have to be carefully designed to travel faster than sound and why air piles up in front of incoming meteroids and compreses to incandescence rather than simply flow out of the way.

 

[flycast]

Thanks. What limits the pressure differentials?

 

[negitron]

The difference in pressure is the amplitude, or loudness, of the sound. The lower limit is, of course, zero PSI since you can't meaningfully have negative pressure. I'm sure there is an upper bound, as well, but I don't know what that might be. Large explosions can have overpressures exceeding 30 PSI which is more than enough to kill you dead.

 

[Cleonis]

Why is the speed of sound fairly constant within the same medium? What keeps it from slowing down or speeding up significantly? What is the principal that limits sound to a fairly narrow speed?

Your question can be generalized to any wave propagation.

Instead of discussing air I will first discuss propagation of a transversal wave along the length of a string under tension, such as a guitar string.

The following may seem like a detour, please bear with me.
When a guitar string is struck the vibration can be thought of as a combination of two transversal waves traveling along the string, in opposite direction. The resultant wave of those traveling waves is a standing wave.

The mass of the string gives the inertial mass, and the tension of the string provides the force that draws back to the equilibrium point. The force that pulls the string back towards equilibrium position is pretty much proportional to the amount of displacement. In general a force with that characteristic is called a 'harmonic force', as it tends to sustain harmonic oscillation.

A harmonic force has the following property: the period of the vibration that it sustains is independent of the amplitude. (Which is a characteristic that you know from string instruments; playing them soft or hard has little effect on the pitch.)

The guitar string: I will refer to the force that pulls the string back towards equilibrium position the 'restoring force'. If you increase the string tension you increase the restoring force, and then the string will vibrate at a higher frequency. This higher frequency corresponds to higher velocity of wave propagation along the string.

Finally, back to sound propagation. The two factors that determine the speed of sound are the density of air (like the mass per unit of length affects the guitar string pitch), and the elastic properties of air: if you compress air, how much does the pressure increase as the volume decreases.

As in the general case of harmonic oscillation: the speed of wave propagation is pretty much independent of the amplitude. That is why the speed of sound in air remains within quite a small range.


I read somewhere that the first scientist to predict the speed of sound from first principles was Isaac Newton. As I understand it he worked along the above lines: given the density of air and the way air responds to compression you can calculate the propagation speed.


Cleonis

 

[KnowPhysics]

i studied somewhere that speed of sound is not dependent upon the sound amplitude, frequency. i have problem here, the frequency = (1/time) if the frquency changes the speed of sound must change. can anyone explain, why what i am saying is wrong?