# Standing Waves

1. Feb 7, 2009

### Nano

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
velocity = wavelength * frequency

3. 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)

Last edited: Feb 7, 2009
2. Feb 7, 2009

### Carid

Take a butchers at this...

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

Last edited by a moderator: May 4, 2017
3. Feb 7, 2009

### AEM

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).

4. Feb 7, 2009

### 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?

Last edited: Feb 7, 2009