Calculate number of nodes in stationary waves

[markus92]

Homework Statement

Hi guys I have this problem that I can't solve..

Suppose to have this situation:

when M=16kg the cord vibrates in one of its normal ways of oscillation.
when M=6.25 we have the same frequency but 3 more nodes.

How many are the nodes of the stationary wave in the first and in the second case?Knowing that for the n harmonic the frequency is

\frac{n}{2L}\sqrt{\frac{T}{u}}

3more node → n harmonic first case +2 so

\frac{n1}{2L}\sqrt{\frac{T1}{u}}=\frac{n2}{2L}\sqrt{\frac{T2}{u}}

but it's wrong.

How can I solve this?

Thanks in advance.

 

[darkxponent]

I think i would be n+3 not n+2 for three more nodes

 

[markus92]

yes I think you're right

edit.

solved

 

[barryj]

I worked the problem and I am curious what the answer is?

 

[markus92]

in the first case it's the 5th harmonic, in the second case 8th, so 6 nodes and 9 nodes.

http://www.wolframalpha.com/input/?i=n*((16*g)/u)^0.5=(n+3)((6.25*g)/u)^0.5+solve+for+n+

 

[barryj]

Let me ask for a definition. If the string is vibrating at its lowest frequency, do you consider the endpoints f the string where it attaches to the wall and pully nodes or do the nodes only exist BETWEEN the end points? Put another way does the fundamental frequency have 0 or 2 nodes?

 

[markus92]

I consider the fundamental have 2 nodes like this schema