Question on a waves/sound problem

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To solve the problem of finding the lowest frequency for standing waves in two strings with different lengths and linear densities, the tension in both strings is given as 190.0 N. The relevant equations include the wave frequency formula f = nv/2L and the relationship between the frequencies and modes of the two strings. The user has identified the lengths and linear densities of the strings but is struggling to calculate the wave speeds (v1 and v2) and establish a ratio between the mode numbers (n1 and n2). The user has made progress by setting up the equation relating the two strings but needs guidance on deriving the wave speeds and the mode number ratio. Understanding these concepts is crucial for determining the lowest frequency that allows for standing waves with a node at the junction.
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Homework Statement


Question: Two strings at different lengths and linear densities are joined together. They are stretched so that the tension in each string is 190.0 N. The free ends are fixed in place. Find the lowest frequency that permits standing waves in both strings with a node at the junction. The standing wave pattern in each string may have a different number of loops.

Homework Equations



3.75 m 1.25m
_________________=====================

6*10^-2 kg/m 1.5*10^-2 kg/m

(this is kinda what the picture looks like if it helps but it seems really confusing on the computer)

Equations I should use (there may be others):
f=nv/2L
(n1v1)/2L1=(n2v2)/2L2

Other information I am given:
L1=3.75
L2=1.25
n1=?
n2=?
v1=?
v2=?
(m/L)=6.00x10^-2 kg/m
(m/L)2=1.50x10^-2 kg/m

I need to create a ratio between n1 and n2.

I don’t understand how I get v and then how to find a ratio between n1 and n2.


The Attempt at a Solution


Well above I listed all the variables I knew and the ones I didn't know. from that I plugged what I had into the second equation and got (n1v1)/2(3.75)=(n2v2)/2(1.25). That is about how far I got. I don’t understand how I get v and then how to find a ratio between n1 and n2.
 
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Sorry the picture got a little messed up on the computer. Hopefully it will be easy to tell where things go based on the other information.
 
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