# Homework Help: Wavelength problem

1. Mar 2, 2013

### PhizKid

1. The problem statement, all variables and given/known data
A uniform string of length 0.5 m. is fixed at one end and free at the other end. Find the wavelength of the fundamental mode of vibration.

2. Relevant equations
λ = (2L) / mode

3. The attempt at a solution
λ = (2(0.5 m.)) / 1
λ = 1 m.

But the solution says it's 2 m. because λ = 4*L. Why is it 4L when the formula is 2L?

2. Mar 2, 2013

3. Mar 2, 2013

### PhizKid

I don't understand why the fundamental is 1/4 wavelength in my problem. Maybe it might help if I understood where the formula λ = (2L) / mode came from, because it's the only one involving wavelength and length that I know.

4. Mar 2, 2013

### Delphi51

I have not seen λ = (2L) / mode but it suggests a string fixed at both ends:
Then mode = 1 would be one wavelength spread over two lengths or half a wavelength on the string length L. At mode = 2, a complete wavelength on the length L. If you draw pictures of these, you'll see that both ends of the string are fixed in each case. See http://www.phys.unsw.edu.au/jw/strings.html.