Fluid Mechanics Help: Sonic Pressure Wave Behavior in Pipes

[Rotormaster]

Hi guys.

I have a question on sonic pressure wave behavior in pipes.

When a pressure wave traversing down a pipe encounters a change in cross-section, namely, a convergence say like that of an expansion chamber, a negative pressure wave is reflected back in the opposite direction. My question is, does the energy of the reflected negative pressure wave proportionally equal the energy that the original wave loses in encountering the convergence?

 

[tiny-tim]

Hi Rotormaster!

… does the energy of the reflected negative pressure wave proportionally equal the energy that the original wave loses in encountering the convergence?

No.

If we treat this as a collision, then of course https://www.physicsforums.com/library.php?do=view_item&itemid=53" of a musical instrument), so we need one extra constraint …

that constraint is the fixed speed of the waves, not their energy.

 

[Juval]

Hi Rotormaster!


No.

If we treat this as a collision, then of course https://www.physicsforums.com/library.php?do=view_item&itemid=53" of a musical instrument), so we need one extra constraint …

that constraint is the fixed speed of the waves, not their energy.

Hi there!

I find this interesting but I don't quite understand what you said.

Obviously, momentum is conserved. And of course, their speed is fixed as we are talking about sonic waves. And, clearly, their energy is obviously not fixed as they are ever engaging in contact with their environment, until they dissipate that is.

But why did you say that the momentum lost by the original wave is equal to the momentum of the reflected wave??

Can you elaborate?

Thanks.

 

[tiny-tim]

Welcome to PF!

Hi Juval! Welcome to PF!

But why did you say that the momentum lost by the original wave is equal to the momentum of the reflected wave??

??

As you said …

Obviously, momentum is conserved.

… and if momentum is conserved, where else can the "lost" momentum go? ​

 

[Juval]

Hi Juval! Welcome to PF!


??

As you said …

… and if momentum is conserved, where else can the "lost" momentum go? ​

Thanks!

Yes, I see what you are saying with that, but that is not what I was referring to.

What I meant was that, a question was asked in the initial post whether the energy of the reflected wave directly equals the energy lost by the original wave. You answered this with a "no"... But then you went on to say that "the momentum lost by the original wave is equal to the reflected wave"??

Hopefully you can explain what you meant by that.

Sorry, I should have made myself clearer from the beginning. :)

 

[tiny-tim]

Hi Juval!

If two tennis balls collide, kinetic energy will always be lost, but momentum will always be conserved.

The momentum lost by one tennis ball will always equal the momentum gained by the other tennis ball.

It's the same with a sound wave …

kinetic energy will be lost (and disappear into other forms of energy)

but the momentum lost by the original wave will equal the momentum gained by the reflected wave.​