Graphing To Find Linear Mass Density (Waves)

[BayernBlues]

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?

 

[BayernBlues]

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?

 

[Moetasim]

I would suggest using a graphing software or program to plot the given equation and determine the slope of the line. This will give you the value of u, the linear mass density of the rope. You can also use the given values for f, n, L, and F to calculate the slope manually and compare it with the graphed value to ensure accuracy.

In terms of the number of graphs, it would depend on the number of different values you have for n, L, and F. If you have multiple values for each, then it would be best to plot a separate graph for each combination of values. This will allow you to see any patterns or trends in the data and make more accurate conclusions about the relationship between f and u. Additionally, plotting multiple graphs will also allow you to check for consistency and accuracy in your results.

It is also important to note that when plotting a graph, it is best to use a large enough range of values for f to ensure that the line is well-defined and the slope can be accurately determined. It may also be helpful to label your axes and include units to make your graph more informative and easier to interpret.

In summary, to find the linear mass density (u) of the rope, you can plot the given equation and determine the slope of the line. It is best to use a graphing software or program and plot multiple graphs to ensure accuracy and identify any patterns or trends in the data.