# This is ! How do I solve the nodes and antinodes for this problem?

1. Nov 20, 2012

### riseofphoenix

HELP!! This is URGENT! How do I solve the nodes and antinodes for this problem??

Last edited: Nov 20, 2012
2. Nov 20, 2012

### H.fulls

Re: This is URGENT! How do I solve the nodes and antinodes for this problem??

Okay so check this diagram out
http://www.physicsclassroom.com/mmedia/waves/h3.gif
Thats a 3rd harmonic...
So you've got 4 nodes where the string is not moving at all, and 3 antinodes of maximum displacement.
Its fixed at each end, so 0m and 9m must be nodes! They cant move if there being held there. So youve got 2 in between , they must be equally spaced so theyve gotta be at 3m and 6m. (Maths way to do this is length/harmonic = 9/3 = 3, gotta be spaced 3m apart)
You know that the antinodes must be halfway between these nodes, so they have to be at 1.5, 4.5 and 7.5! This is length/2*harmonic.

For the frequency...
velocity = root(tension/(mass/length))
and then to get the frequency this must be divided by twice the length :)
Hope you understood all that!!

3. Nov 20, 2012

### H.fulls

Re: This is URGENT! How do I solve the nodes and antinodes for this problem??

sorry thats v = $\sqrt{\frac{T}{M/L}}$

so

f = $\frac{\sqrt{\frac{T}{M/L}}}{2L}$

4. Nov 20, 2012

### PeterO

Re: HELP!! This is URGENT! How do I solve the nodes and antinodes for this problem??

That equation gives you the correct answer, but you then interpreted incorrectly.

The modes of vibration of a string represent STANDING WAVES on the string. The wavelength of a standing wave is 1/2 the wavelength of the travelling wave "causing" the standing wave.

Your formula gives λ = 6m. That is the travelling wave λ

So the wavelength of the standing wave is 3m

The first node is at the fixed end where you start. The next ones are every 3 m from there - until you have reached the other end.

The anti-nodes are halfway between each of those nodes