Standing waves/Nodes

[tandoorichicken]

A string stretched between two supports sets up standing waves with two nodes between the ends when driven at a frequency of 230 Hz. At what frequency will it have three nodes? What order harmonic is such a wave? What is the fundamental frequency?

For the first question, I don't have anything to start with. The problem doesn't give the distance between the supports, the amplitude or anything.

For the second question, what is the definition of 'order harmonic?'

The last question I think I can figure out if I solve the first one.

[Adrian Baker]

Originally posted by tandoorichicken
A string stretched between two supports sets up standing waves with two nodes between the ends when driven at a frequency of 230 Hz. At what frequency will it have three nodes? What order harmonic is such a wave? What is the fundamental frequency?

For the first question, I don't have anything to start with. The problem doesn't give the distance between the supports, the amplitude or anything.

For the second question, what is the definition of 'order harmonic?'

The last question I think I can figure out if I solve the first one.

Have you tried drawing it out?

With two nodes between the ends (and one other at each end) you have four nodes in total - so you must have 1.5 complete wavelengths. This is a second harmonic (draw out a system with two nodes, three nodes, four nodes etc) two nodes is the fundamental, three nodes the first harmonic and so on.

You don't need the amplitude, and as the distance between the supports is constant, you don't need to know that either.