# Waves on a String 1

1. Feb 12, 2004

### tandoorichicken

A steel wire is stretched taut between supports one meter apart. What is the fundamental wavelength of vibration of the wire?

2. Feb 13, 2004

### chroot

Staff Emeritus
Begin by defining "fundamental."

- Warren

3. Feb 13, 2004

### HallsofIvy

Staff Emeritus
Since the wave is fixed at the two poles, the wave must have 0 value at those two points. The standard sine wave (wave length 2pi) is 0 at 0, pi, and 2pi. A wave of wave length l will be 0 at 0, l/2 and l. In particular, the longest wave (which I take is what you mean by "fundamental wavelength") that is 0 at 0 and 1 must have wavelength 2.

4. Feb 14, 2004

### tandoorichicken

I get it, so the only way for it to have a wavelength of 1 m is if there was a node in the wire, and then it would have to have some slack, which it doesnt.

Thanks.

5. Feb 17, 2004

### HallsofIvy

Staff Emeritus
No, it is quite possible for the wire to have a node in the center without "slack" (it has to be under tension and able to stretch in order to form waves). You asked for the fundamentalwavelength which is the longest wavelength (lowest frequency). It is possible for the wire to have arbitrarily small wavelength waves ("harmonics").