# Transverse waves on pulley - question

1. Mar 20, 2012

### 3psilon

1. The problem statement, all variables and given/known data
1) an aluminium wire, of length L1 = 60.0 cm, cross sectional area 1.00 x 10^-2 cm^2, and density 2.60 g/cm^3, is joined to a steel wire of length L2, of density 7.80 g/cm^3 and the same cross sectional area. The compound wire, loaded with a block of mass m = 10.0 kg, is arranged so that the distance L2 from the joint to the supporting pulley is 86.6 cm. Transverse waves are set up in the wave using an external source of variable

a) find the lowest frequency of excitation for which standing waves are observed such that the joint in the wire is a node
b) How many nodes are observed at this frequency?

2. Relevant equations

f1= 1/2L * √(T/mu)

3. The attempt at a solution
So far, I know to find tension by basic Ft=Fg
I'm having trouble understanding the theory of it, there will be discontinuity because the change in linear density, but how can I account for that? Also, if there is a node where the lin. density changes, is the discontinuity relevant?

i also tried using percents for my linear density, i.e. 1.466 m = total length of the wire to the pulley, so then 41% of the wire is made up of aluminium, so the linear density could be written as mu = mualuminium + musteel, with adjusted linear density based on the percent

Last edited: Mar 20, 2012
2. Mar 20, 2012

### emailanmol

I am having trouble understanding the description of your system.

How are the strings tied to pulley?

Can you post a picture?

Also is value of L2 given?

3. Mar 20, 2012

### emailanmol

4. Mar 20, 2012

### emailanmol

Ok.I think i understood the problem and have got the answers.(In case you have the final answer let me know so that I can cross check if my answers are right)

there is no discontinuity at the joint.
Its just that at the junction u(linear density)changes, so the velocity changes , similar to cases like refraction of light.

Now,

Since the masses of strings are negligible in comparison to the block you can ignore the change in tension due to weight of strings.
So tension in both strings comes out be nearly mg(m is mass of block).
(the difference is about 10^(-10) which can be ignored)

now what is the ratio of frequency in the two strings?(fairly simple question.)

Now what is ratio of velocities on the two strings?(Remember tension is same.Linear densities are different.)
What are ratio of wavelengths?

(Use v=lambda*f)

If you got these read further.
If you didn't,don't worry.We will focus on the things discussed above first and then move ahead :-)

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Suppose now the no. of loops in string 1 is n and string 2 is k.
What is the relation between lambda1, L1 and n?
Similarly what is the relation for string 2?

For minimum frequency, should n and k be large or small?

Last edited: Mar 20, 2012