Solving Standing Waves/Nodes: 230 Hz, Harmonic Order, Fundamental Freq

[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.

 

[M98Ranger]

To answer the first question, we need to use the equation for the frequency of a standing wave, which is f = n(v/2L), where n is the harmonic order, v is the speed of the wave, and L is the length of the string. Since we are given the frequency (230 Hz) and the number of nodes (2), we can rearrange the equation to solve for the length of the string: L = (n/2)(v/f). Without knowing the distance between the supports or the amplitude, we cannot determine the length of the string and therefore cannot calculate the frequency for three nodes.

For the second question, the order harmonic refers to the number of times the fundamental frequency (first harmonic) is multiplied. In this case, since we are looking for the frequency with three nodes, it would be the third harmonic.

To find the fundamental frequency, we can use the equation f = v/2L, where v is the speed of the wave and L is the length of the string. Without knowing the length of the string, we cannot determine the fundamental frequency.

In summary, without more information, we cannot accurately determine the frequency for three nodes or the fundamental frequency. The problem would need to provide either the length of the string or the amplitude for us to solve for these values.