What is the equation for standing wave patterns and why is the solution 0?

[Tohoshi]

Homework Statement

Hi everyone. I am working on a physics research paper on Standing Wave Patterns and the physics of a viola. I found this formula for standing wave patterns and am having trouble making sense of it. When I tried, I got sin(0) which is 0 making the whole thing 0. Is this a valid equation and am I missing something?

w = 2764
t = (1/440)

k = 2pi/wavelength
x = distance traveled.

I am sorry, but I am really confuesed

Homework Equations

y = 2yocos(wt)sin(Kx)

The Attempt at a Solution

2yo (2764)(1/440) = 2p1
cos 2 pi = 1
sin (0) = 0

= Ahh!

I may be using the variables wrong, but I used 2pi * frequency to get w, 1/frequency to get t

 

[Feldoh]

y(x,t) = 2yocos(wt)sin(Kx) is the function which is dependent on both time and position. t is not the period.

It's perfectly reasonable to get 0 a nodal points.

 

[Delphi51]

I don't know the formula y = 2yocos(wt)sin(Kx) so perhaps I shouldn't be offering any help.
But it seems clear to me that the sin(kx) = 0 at x = 0 is just telling you that there is no vertical movement of the string at x = 0. That would be the position where the string is attached. It seems a very reasonable result!

 

[Tohoshi]

Okay. Thanks.

Excuse my ignorance, we had to research a topic that we haven't covered, but would it be more appropriate to use x as the string length, since that is further from where the string is attached and would cause vertical movement? I am not really understanding what I proved by getting 0...well I don't really understand what I am proving anyway.

 

[Feldoh]

The equation you listed is modeling a string in two dimensions that is time dependent. So you can think of the function giving you the height of the string at some distance x, and some time t.

x and t are variables that change.

You proved that when sin(kx) = 0 then the height of the string is also 0. This makes sense since at x=0 there is a node.