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

[riseofphoenix]

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

For nodes, I tried doing λ = 2L/n but it's not giving me the answers they got... please help!

 

[H.fulls]

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 can't move if there being held there. So youve got 2 in between , they must be equally spaced so theyve got to be at 3m and 6m. (Maths way to do this is length/harmonic = 9/3 = 3, got to 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!

 

[H.fulls]

sorry that's v = $\sqrt{\frac{T}{M/L}}$

so

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

 

[PeterO]

For nodes, I tried doing λ = 2L/n but it's not giving me the answers they got... please help!

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 traveling wave "causing" the standing wave.

Your formula gives λ = 6m. That is the traveling 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

 

[Nickie]

Hello, solving for nodes and antinodes can be a bit tricky, but I can provide some guidance to help you solve this problem. Firstly, it is important to understand the concept of nodes and antinodes. Nodes are points along a standing wave where there is zero displacement, while antinodes are points where there is maximum displacement.

To solve for nodes and antinodes, you will need to know the wavelength (λ), the length of the standing wave (L), and the number of nodes (n). The formula you mentioned, λ = 2L/n, is correct. However, it is important to note that this formula only applies to a specific type of standing wave known as the fundamental mode. If you are dealing with higher modes, the formula will change.

To ensure you are using the correct formula, it is important to first identify the type of standing wave you are dealing with. For example, the fundamental mode has only one node and two antinodes, while the second harmonic has two nodes and three antinodes. Once you have identified the type of standing wave, you can use the appropriate formula to solve for the nodes and antinodes.

If you are still not getting the correct answers, it could be due to a calculation error or not using the correct units. Make sure to double-check your calculations and use consistent units throughout. If you are still having trouble, I recommend seeking help from your teacher or a tutor who can guide you through the process and check your work. I hope this helps. Good luck!