Graphing To Find Linear Mass Density (Waves)

AI Thread Summary
To determine the linear mass density (u) of a rope in a lab experiment involving standing waves, the equation f = n/2L[sqrt(F/u)] is used. By rearranging this equation, the slope of the graph plotting f against n/2L[sqrt(F)] can provide the value for u, as the slope is related to the square root of u. It is suggested to plot multiple graphs for varying values of n, L, and F to analyze their effects on the relationship. Fixing sqrt(F)/2L allows for using n (the harmonic number) as the x-values in the graph. Ultimately, the slope of the graph will correspond to 1/sqrt(u), leading to the conclusion that the slope is inversely related to the linear mass density.
BayernBlues
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Homework Statement



This is for a lab involving a rope being tied to a frequency generator on one end and a mass string on the other (creating tension on the rope) in order to create standing waves.

I have to find the u (linear mass density which is kg/m for a rope by plotting it. This is the equation I'm supposed to plot f vs n/2L[sqrt(F)]

I have the value for f (frequency), n, L (length), and F (tension in the string) so all I have to do is find u. I'm unsure however how plotting the above relation will give me the value for u using various frequencies.

Homework Equations



f = n/2L[sqrt(F/u)]

where:
f = frequency (hz)
n = integer such as 1, 2, 3
L = length such as 0.100 m
F = Force of tension on the rope in N (mass*gravity)
u = Linear mass density (kg/m or mass/length of rope)

The Attempt at a Solution



Rearranging the equation, I'm guessing u would be the slope in the relation above. And the slope will equal 1/sqrtu ? Also how many graphs should I draw if I have a changing value for n, L, and F? Would it be a separate graph for each different value of L and F?
 
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If I fix sqrtF/2L then can I use n (harmonics) for the x values?

Also, would the slope of the graph equal 1/u?
 

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