# Homework Help: What is the speed of the string? (wave problem)

1. Jan 23, 2013

### bored2death97

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

A wave travels along a spring at speed v0. What will be the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius.

2. Relevant equations

v=√(T/μ)
speed= square root of (tension divided by mu)

μ=m/L
mu= mass/length

3. The attempt at a solution

With the first equation I filled in the equation for mu. Assuming twice the radius would mean twice the mass, I multiplied mass by 2.

v=√[T/(2m/L)]

v=√(TL/2m)

Then if I were to take the value of 2 out of the square root, I would get v=0.707[√(TL/m)]

Rearrange and get v/0.707

So where did I go wrong??

2. Jan 23, 2013

### Dick

Twice the radius doesn't mean twice the mass. If you double the radius of a circle by what factor does the area increase?

3. Jan 23, 2013

### bored2death97

It increases by a factor of 4. Thank you.