Which Pulse Reaches the Knot First?

[logix24]

Homework Statement

Two strings have been tied together with a knot and stretched between two rigit supports. The strings have linear densities µ1 = 1.4 x 10-4 kg/m and µ2 = 2.8 x 10-4 kg/m. Their lengths are L1 = 3.0m and L2 = 2.0m, and string one is under 400N tension. If a pulse is started simultaneously on each string, traveling towards the knot, which pulse reaches the knot first?

Homework Equations

v=√(T_s/μ)

The Attempt at a Solution

v1=√(400N/(1.4 x 10^-4 kg/m)=1690m/s)
v2=√(400N/(2.8 x 10^-4 kg/m)=1195m/s)

v1 should be faster, but I know that I'm missing something in my equations. We've been given the two lengths of the strings and the tension of only one string, so how do I utilize the value of the lengths in my formula?

 

[pam]

Time=dist/v.
The knot doesn't move. What does that say about the tension in each strilng?

 

[logix24]

Does the tension remain the same in each string?

 

[pam]

Yes, the two forces on the knot must cancel.

 

[logix24]

So then why does the question give the two lengths of the string and do I use the values of Length in solving the problem?

 

[pam]

time=length divided by speed.