What is the length of a vibrating metal wire at its third harmonic frequency?

[goonking]

Homework Statement

A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire.

Homework Equations

The Attempt at a Solution

I don't quite understand the question, it says 0.32m from one end, is that from the start to the first node?

the amplitude going to be 1/4 its maximum where sin(x) = 0.25, correct?

 

[haruspex]

A metal wire is vibrating at its third-harmonic frequency. 0.32 m from one end, the amplitude is equal to one quarter the maximum amplitude. Find the length of the wire.

It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.

the amplitude going to be 1/4 its maximum where sin(x) = 0.25, correct?

It depends what you mean by x.

 

[goonking]

It is not clear to me whether the wire is fixed at either or both ends. I'd guess it's fixed at both. If so, the 'start' is a node, and .32m is the distance from there to the given point.

It depends what you mean by x.

if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."

 

[haruspex]

if it helps, the hint the question has is : "The third harmonic will have a wavelength equal to 2/3 of the length of the string. Also, *note to self* the max-amplitude of this wave is (2A) not (A)."

So what does that tell you about whether one or both ends of the string are nodes?