# Another Simple Physics Problem

#### freeofwork

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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#### LawrenceC

Hint: You know the diameters so you know the mass per unit length of each.

#### freeofwork

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...

#### LawrenceC

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.

#### freeofwork

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...

#### LawrenceC

m/l is mass per unit length.

#### LawrenceC

What's the formula for the volume of a cylinder?

#### LawrenceC

That's correct or you could also say (pi d^2/4)h. So what would be the mass per unit length?

#### freeofwork

x being the tension?..

#### LawrenceC

Do you know what mass per unit length means?

linear density

#### LawrenceC

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.

#### LawrenceC

Got to hurry here. Giants-Falcons game starts in 11 minutes!

#### freeofwork

how do you find the density or linear density? this is crazy

#### LawrenceC

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.

#### LawrenceC

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.

#### freeofwork

what do u mean by mass per unit ratios?

#### LawrenceC

(M1/Ll)/(M2/L)

M's are dependent on diameters. L's drop out.

#### freeofwork

o how would u get e mass?
so the equation who look something like this?
v1/v2=√m1m2

#### LawrenceC

You almost have it. Check your algebra. The radical should be m2/m1. Relate the m's to their respective diameters....

#### freeofwork

i dont know how the mass are related to the diameters...

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