Calculating Next 3 Harmonics of a Standing Wave

[Nano]

Homework Statement

Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?

Homework Equations

velocity = wavelength * frequency

The Attempt at a Solution

I don't understand how to draw the "next harmonic". I've come up with a formula for wavlenth of the first harmonic:
= (4/3)L
and with that, frequency
= (3v)/(4L)

 

[Carid]

Take a butchers at this...

http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html"

 

[AEM]

Homework Statement

Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?

Homework Equations

velocity = wavelength * frequency

The Attempt at a Solution

I don't understand how to draw the "next harmonic". I've come up with a formula for wavlenth of the first harmonic:
= (4/3)L
and with that, frequency
= (3v)/(4L)

Well, for a standing wave the ends are fixed and therefore are nodes. In a sinusoidal wave the nodes are half a wavelength apart. In a string of length L, standing vibrations may be set up by different frequencies that give rise to waves that will have nodes at the endpoints. These wave will have wavelengths,

\lambda = 2L, \frac{2L}{2}, \frac{2L}{3},..., \frac{2l}{n}

The wave speed c is the same for all frequencies, and as you say, c = f \lambda

This should be enough for you to deduce the frequencies and the wavelengths of the harmonics (or overtones as they are sometimes called).

 

[Nano]

So as I've said that the wavelength of the first harmonic =(4/3)L, that means the wavelength of the second harmonic
= (4/3)L / n = (4/3)L / 2 = (2/3) L

Is this right?

By the way, the wave has a node at one end and is open at the other. In class we learned that standing waves with one open/one fixed end have only odd numbered harmonics. Why is this?