# Question about waves (velocity, tension)

## Homework Statement

Two steel wires are stretched with the same tension. The first wire has a diameter of 0.580mm and the second wire has a diameter of 0.88mm. If the speed of waves traveling along the first wire is 54m/s, what is the speed of waves traveling along the second wire?

## Homework Equations

v=sqrt.(F/miu) (miu is mass/length)

## The Attempt at a Solution

I tried to make a proportion. 0.58/54=0.88/x. I got the incorrect answer, though. The answer should be 35.6m/s.

rude man
Homework Helper
Gold Member

## Homework Statement

Two steel wires are stretched with the same tension. The first wire has a diameter of 0.580mm and the second wire has a diameter of 0.88mm. If the speed of waves traveling along the first wire is 54m/s, what is the speed of waves traveling along the second wire?

## Homework Equations

v=sqrt.(F/miu) (miu is mass/length)

## The Attempt at a Solution

I tried to make a proportion. 0.58/54=0.88/x. I got the incorrect answer, though. The answer should be 35.6m/s.
Why a proportion? That is not the formula for speed of waves in a wire with linear density μ under tension F.

mfb
Mentor
There is a square root in the equation. Density (mass/length) is proportional to the squared velocity, not the velocity itself.

Okay, but then what should I do?

There is a square root in the equation. Density (mass/length) is proportional to the squared velocity, not the velocity itself.
I know. I put the formula as v=sqrt. (F/miu)

Oh alright I see what you are saying. So a proportion is not the way to go here. But what should I do? I feel like I'm missing the information. Don't I need force or mass?

rude man
Homework Helper
Gold Member
I know. I put the formula as v=sqrt. (F/miu)
v = sqrt(F/μ) is correct. Did you still not get the right answer? Are your units consistent?

v = sqrt(F/μ) is correct. Did you still not get the right answer? Are your units consistent?
I don't think I am solving it right

mfb
Mentor
So a proportion is not the way to go here
A ratio is a good idea, but you cannot use the velocity directly, you have to use the squared velocity (=a quantity proportional to μ).

rude man
Homework Helper
Gold Member
I don't think I am solving it right
What did you get for v?

You are on the right track. The mass per unit length is PRORTIONAL to the diameter squared.
The mass per unit length of the 0.88mm dia wire is (0.88/0.58) squared = 2.3
Use this in your equation for speed (dont forget the square root !!!!) and you should get 35m/s