Understanding Nodes and Frequencies in a Uniform String Under Tension

[tourjete]

Homework Statement

A uniform string of length 2.5 m and mass 0.01 kg is placed under a tension of 10 N.

1. What is the frequency of the fundamental mode?

2. If the string is plucked and is then touched at a point 0.5 m from one end, creating a node, what frequencies persist?

Homework Equations

\omega = \sqrt{T/\mu}* n\pi/L where \mu = M/L

The Attempt at a Solution

I got the first part, I just plugged all the given information into the equation and used n=1 since it asked for the fundamental mode. I got 62.8319 radians/second.

I'm a bit lost as to what the concept of a node is. Do I just use the same equation again, but use L = 2.5 - .5 = 2 m? Or do I use n=5 since the string is now divided into fifths?

 

[ehild]

Supposed the string is fixed at both ends, its length is equal to a half-wave in the fundamental mode. There is no motion at a node. Draw the standing wave when there is a node at 0.5 m from one end. Where are the other nodes?

ehild