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Another Simple Physics Problem

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

Two steel wires are stretched with the same tension. The first wire has a diameter of .00059 meters and the second wire has a diameter of .00089m. If the speed of waves traveling along the first wire is 54.0 m/s, what is the speed of the waves along the second wire?

2. Relevant equations

v=√Ft/μ
μ=m/L


3. The attempt at a solution

I have no idea how to get the mass or length of the string...
 
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Hint: You know the diameters so you know the mass per unit length of each.
 
Hint: You know the diameters so you know the mass per unit length of each.
what would be the equation for that... i only know μ=m/L...
 
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You know the formula for velocity. The tension is the same for both wires. Mu is mass per unit length which you can determine by realizing that a wire is a cylinder. You know the velocity of the wave on one of the wires. Therefore, you can solve this without knowing the respective wire lengths.
 
You know the formula for velocity. The tension is the same for both wires. Mu is mass per unit length which you can determine by realizing that a wire is a cylinder. You know the velocity of the wave on one of the wires. Therefore, you can solve this without knowing the respective wire lengths.
imdont have e height though... how can you convert the diameter into something usable...
 
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m/l is mass per unit length.
 
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What's the formula for the volume of a cylinder?
 
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That's correct or you could also say (pi d^2/4)h. So what would be the mass per unit length?
 
radical x over 54^2?
x being the tension?..
 
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Do you know what mass per unit length means?
 
linear density
 
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In the case of a wire which is a cylinder the mass per unit length is:

m/L = rho * Volume/L = rho * pi * d^2/4 * L/L = rho * pi * d^2/4

where rho is the density in kg/meter^3.

You have the formula for the velocity of one wave at a specific m/L. You want the velocity of the wave in the other wire. The tensions are the same.

V1^2 = F/mu1 and V2^2 = F/mu2. Think about (V1/V2)^2.
 
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Got to hurry here. Giants-Falcons game starts in 11 minutes!
 
how do you find the density or linear density? this is crazy
 
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You do not the actual number; you only need the ratio of the two.

V1^2 = F/mu1 and V2^2 = F/mu2. Think about (V1/V2)^2.
 
idk....
 
i dont know.
 
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Ok, I shall provide more help. I cannot do it for you -forum rules.

Form a ratio for v1/v2. You know one of the v's. This ratio equals square root of mass per unit length ratios. You can compute this ratio. This leaves one unknown.
 
what do u mean by mass per unit ratios?
 
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(M1/Ll)/(M2/L)

M's are dependent on diameters. L's drop out.
 
o how would u get e mass?
so the equation who look something like this?
v1/v2=√m1m2
 
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You almost have it. Check your algebra. The radical should be m2/m1. Relate the m's to their respective diameters....
 
i dont know how the mass are related to the diameters...
 

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