Understanding Sound Cavity for Greenhands

[genxium]

Homework Statement

No specific question, I'm a greenhand to waves, so when it came to sound cavity, I was just confused how the teacher(in the video lecture,I'm not a physics major) can distinguish which side is a node and which is an anti-node, it seems too fast for me, could anyone give me a hand?

Like give p(z,t)=(Acos(kz)+Bsin(kz))cos(wt), inside a 1 end open,1 end closed cylinder cavity, the teacher just assumed a new variable, say q, referring to the deviation of air molecules , and I just didn't know what p stands for ? I supposed that p was for the deviation of air molecules before q jumps out >_<

Homework Equations

The 1 dim wave equation? I'm afraid I'm totally confused what x in $\frac{\partial x^2}{{\partial}^2 z}=\frac{\partial x^2}{v^2 {\partial}^2 t}$ refers to.

The Attempt at a Solution

Not yet quite understand anything >_<

 

[BruceW]

This shouldn't really be in the homework section. (So that you know where to post in the future). A question like this should really go in the classical or general physics section. The reason is that we're not allowed to give too much help in the homework section. So if I started telling you as much as I could about sound waves, I might get banned. (Which is fair enough).

I'm guessing this isn't really homework, and you'd like some extra explanation of what the teacher was talking about?

 

[ehild]

P is local pressure of the air and q is the displacement of the molecules at a given point of the pipe. At the node of P there is antinode of q and vice versa. See: http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html

ehild

 

[genxium]

I'm guessing this isn't really homework, and you'd like some extra explanation of what the teacher was talking about?

Thanks for you advice, as you may see, every time I try to post something in a section other than "homework", there's a red line warning making me hesitate if I should really post it in "homework" section or not, and I think this problem might be involved in someone's homework >_<

 

[genxium]

P is local pressure of the air and q is the displacement of the molecules at a given point of the pipe. At the node of P there is antinode of q and vice versa. See: http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html

ehild

Thanks ehild, this really helps ！

 

[BruceW]

$$\frac{\partial x^2}{{\partial}^2 z}=\frac{\partial x^2}{v^2 {\partial}^2 t}$$
I don't know what this means either. But I do know that:
$$\frac{\partial^2 P}{{\partial z}^2}=\frac{1}{v^2} \frac{\partial^2 P}{{\partial t}^2}$$
Is the acoustic wave equation (for sound, in 1D). And in the equation, P is the difference between local pressure and ambient pressure. P is often called 'acoustic pressure'.

When it comes to nodes and anti-nodes, it is important to remember that a node for molecule displacement is an anti-node for acoustic pressure. And an anti-node for molecule displacement is a node for acoustic pressure.

The open end of the cylinder must be a node for acoustic pressure because the local pressure must equal the ambient pressure. And at the closed end of the cylinder, we know the molecule displacement must go to zero. So the closed end is a node for molecule displacement, and therefore an anti-node for acoustic pressure.