# Homework Help: Youngs Modulus and Standing Waves combined question

1. Mar 17, 2013

### phoebz

The figure shows an aluminum wire of length L 1 = 60.0 cm, cross-sectional area 1.00 x 10-2 cm2, and density 2600 kg/m3, joined to a steel wire of density 7.80 g/cm3 and the same cross-sectional area. The compound wire, loaded with a block of mass 10.0 kg, is arranged so that the distance L 2from the joint to the supporting pulley is 86.6 cm. Transverse waves are set up on the wire by an external source of variable frequency; a node is located at the pulley. [Hint: You may want to calculate the ratio of the number of loops in the steel compared to the aluminum. Then surmise which numbers will give you the desired lowest frequency.]

-What is the lowest frequency that generates a standing wave pattern that has the joint as one of the nodes?

*Youngs Modulus --> Aluminium: 7x10^10
Steel: 20x10^10 kg/m^3

My Attempt:

Y= (F/A)/(ΔL/L)
-The force put on both strings will be equal so I tried setting the two wire equations equal as
YAΔL/L (for aluminium) = YAΔL/L (for steel)

I was trying to find the length of the other string but I got stumped because I did have the change in length for either string.

I needed the length of each string for the equation μ=mass/length because v=√(F/μ) and frequency equals velocity/λ.

#### Attached Files:

• ###### Screen shot 2013-03-17 at 6.55.03 PM.png
File size:
4.3 KB
Views:
155
2. Mar 17, 2013

### TSny

You can get the linear mass density μ from the volume mass density ρ and the cross-sectional area A. Consider a section of a wire of length L. Can you find an expression (in symbols, not numbers) for the mass of the section in terms of ρ, A, and L? Use this expression for the mass to determine an expression for μ in terms of ρ and A.