Which Pulse Reaches the Knot First?

AI Thread Summary
The discussion revolves around determining which pulse reaches a knot first when two strings with different linear densities are tied together and stretched under tension. The calculated wave speeds for the two strings are 1690 m/s for the first string and 1195 m/s for the second string, indicating that the first string is faster. However, the tension in both strings remains equal at the knot due to the forces canceling out. The lengths of the strings are relevant for calculating the time it takes for each pulse to reach the knot, as time is derived from the distance divided by speed. Understanding the relationship between tension, wave speed, and string length is crucial for solving the problem accurately.
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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?
 
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Time=dist/v.
The knot doesn't move. What does that say about the tension in each strilng?
 
Does the tension remain the same in each string?
 
Yes, the two forces on the knot must cancel.
 
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?
 
time=length divided by speed.
 
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