Question about waves (velocity, tension)

  • #1

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.
 

Answers and Replies

  • #2
rude man
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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.
Why a proportion? That is not the formula for speed of waves in a wire with linear density μ under tension F.
 
  • #3
35,139
11,390
There is a square root in the equation. Density (mass/length) is proportional to the squared velocity, not the velocity itself.
 
  • #4
Okay, but then what should I do?
 
  • #5
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)
 
  • #6
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?
 
  • #7
rude man
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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?
 
  • #8
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
 
  • #9
35,139
11,390
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).
 
  • #11
210
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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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