Fundamental frequency of oscillation in 2 ropes

[goonking]

Homework Statement

Homework Equations

The Attempt at a Solution

if the material are the same in both strings, then the density should be the same.
v = sqrt (tension/μ)

tension in the first string should be 30 kg x 9.8 m/s^2 = 294 N

next,

v = λƒ

and string#2 needs to have twice the frequency of string#1

and this is where I am stuck, don't know where to proceed from here

do I need wavelength here? if so, how would i find it?

 

[haruspex]

You have two equations involving v, but you are not very interested in v. So what should you do with the two equations?
Next, you have the same equations for two different cases. Some of the variables are the same for both cases. It helps to clarify things if you create different symbols (like T₁, T₂) wherever the variables are different. That should produce two equations, neither involving v.

 

[goonking]

You have two equations involving v, but you are not very interested in v. So what should you do with the two equations?
Next, you have the same equations for two different cases. Some of the variables are the same for both cases. It helps to clarify things if you create different symbols (like T₁, T₂) wherever the variables are different. That should produce two equations, neither involving v.

do I equate them both? :

λƒ = sqrt (tension/μ) ?

also, what is interchangeable in each string with masses? do they both have the same wavelength? do they have the same velocity?

 

[haruspex]

do I equate them both? :

λƒ = sqrt (tension/μ) ?

also, what is interchangeable in each string with masses? do they both have the same wavelength? do they have the same velocity?

You know the tensions (different) and the wavelengths (different). You know the frequencies are different. What does that leave?

 

[goonking]

You know the tensions (different) and the wavelengths (different). You know the frequencies are different. What does that leave?

velocity? but if tension is different then velocity should be different too, right?

 

[haruspex]

velocity? but if tension is different then velocity should be different too, right?

We eliminated velocity. Look at your equation in post #3. The are four variables in there. Which one has not been mentioned?