Finding the frequency of a string based on Mass and Tension

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The discussion revolves around calculating the frequency of a string using the formula ƒ=sqrt(T / u) / 2L. The user calculated tension (T) as 490N and linear mass density (u) as 0.04285 kg/m, leading to a frequency of 76.38Hz. There is confusion regarding the division by 2L, questioning if it was necessary or if the original answer omitted this step. Additionally, the user raises a point about whether the wave can freely vibrate over the entire 70 cm length, considering the effects at the pulley. Clarification on these calculations and assumptions is sought.
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I saw the following problem in a test I was reviewing:
1641660422506.png

I don't understand how they got their answer. I used the formula: ƒ=sqrt(T / u) / 2L where f is the frequency of the string, T is the tension, u is the linear mass density, and L is the length of the string.
I got:
T = mg = 50 * 9.8 = 490N
u = m/l = 3/7 g/cm = 0.04285 kg/m
L = 70cm = 0.7m
Therefore f = sqrt(490 / 0.04285) / 1.4 = 106.93 / 1.4 = 76.38Hz. I see that they got their answer from the first part, but did they forget to divide by 2L, or was I not supposed to do that? Thanks!
 
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Can the wave freely vibrate over the entire 70 cm length? Think about what happens at the pulley.
 
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