Question about waves (velocity, tension)

[NicoleRosalyn]

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 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]

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

 

[NicoleRosalyn]

Okay, but then what should I do?

 

[NicoleRosalyn]

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)

 

[NicoleRosalyn]

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]

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?

 

[NicoleRosalyn]

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]

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]

I don't think I am solving it right

What did you get for v?

 

[Emilyjoint]

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