Waves on a String 1

[tandoorichicken]

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

[chroot]

Begin by defining "fundamental."

- Warren

[HallsofIvy]

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.

[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.

[HallsofIvy]

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").