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Finding Frequencies in Two Strings Stuck Together

  • Thread starter Hypnos_16
  • Start date
153
1
1. Homework Statement

Two strings have different lengths (L1 = 3.920 m and L2 = 1.960 m) and linear densities (mL1 = 2.64E-1 kg/m and mL2 = 6.60E-2 kg/m), as the drawing below shows.

|.........................................|
|.........................................|
|----------------------------------|
|.........................................|
|.........................................|
(Okay, only the "-"s are the line, it's pretty much just two strings that are stuck together, with different linear densities)

They are joined together and stretched so that the tension in each string is 192 N. The free ends of the joined string 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.

L1 = 3.92 m
L2 = 1.96 m
mL1 = 0.264 kg/m
mL2 = 0.0660 kg/m
T = 192 N

2. Homework Equations

v = √(T / µ)
v = ƒ (Landa)

3. The Attempt at a Solution

v = √(T / µ)
v = √(192 / 0.264)
v = 27.0 m

v = √(T / µ)
v = √(192 / 0.0660)
v = 54.0 m

I found the speed in both strings using their proper linear density. After getting two speeds and having two different wavelengths resulting in two completely different frequencies. Then i realized perhaps the speed should be the same, since they're attached. But even then the frequency isn't the same.

Help?
 

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