Graphing To Find Linear Mass Density (Waves)

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SUMMARY

This discussion focuses on determining the linear mass density (u) of a rope by plotting the relationship between frequency (f) and the expression n/2L√F. The equation f = n/2L√(F/u) is central to the analysis, where f represents frequency in Hz, n is an integer, L is the length of the rope in meters, and F is the tension force in Newtons. The participants conclude that the slope of the graph will indeed relate to the linear mass density, specifically suggesting that the slope equals 1/√u, and they discuss the implications of varying values for n, L, and F in their plots.

PREREQUISITES
  • Understanding of wave mechanics and standing waves
  • Familiarity with linear mass density concepts
  • Basic knowledge of graphing and slope interpretation
  • Proficiency in manipulating algebraic equations
NEXT STEPS
  • Research how to plot frequency vs. harmonic number for wave equations
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  • Explore the concept of harmonic frequencies in standing wave systems
  • Investigate the effects of varying tension and length on wave properties
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Students in physics or engineering courses, particularly those involved in laboratory experiments related to wave mechanics and linear mass density calculations.

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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