Question about waves (velocity, tension)

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Homework Help Overview

The discussion revolves around the speed of waves in two steel wires under the same tension, focusing on the relationship between wire diameter, mass per unit length, and wave speed. Participants are examining the implications of the wave speed formula in the context of differing wire diameters.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of proportions to relate the diameters and wave speeds, questioning the validity of this approach. There is discussion about the correct application of the wave speed formula and the role of mass per unit length.

Discussion Status

There is ongoing exploration of the correct method to relate the wave speeds of the two wires. Some participants have pointed out the need to consider the square of the velocities in relation to mass per unit length, while others express uncertainty about the information needed to proceed.

Contextual Notes

Participants note a potential lack of information regarding force or mass, which may be necessary for a complete solution. The discussion reflects confusion about the application of the wave speed formula and the relationship between diameter and mass per unit length.

NicoleRosalyn
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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.
 
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NicoleRosalyn said:

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.
 
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?
 
mfb said:
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?
 
NicoleRosalyn said:
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?
 
rude man said:
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
 
NicoleRosalyn said:
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).
 
  • #10
NicoleRosalyn said:
I don't think I am solving it right

What did you get for v?
 
  • #11
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
 

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