# Graphing To Find Linear Mass Density (Waves)

• BayernBlues
In summary, the conversation is about a lab involving a rope, frequency generator, and mass string to create standing waves. The goal is to find the linear mass density (u) by plotting the equation f = n/2L[sqrt(F/u)] with given values for f, n, L, and F. The slope of the graph is expected to be 1/sqrt(u), and it is unclear how many graphs should be plotted with changing values for n, L, and F. The question also arises if the slope of the graph is equal to 1/u and if n (harmonics) can be used for the x values.
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?

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?

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.

## 1. What is linear mass density and how is it related to waves?

Linear mass density is a physical quantity that represents the mass of a one-dimensional object per unit length. In the context of waves, it is often used to describe the mass per unit length of a string or wire that is being vibrated to produce a wave.

## 2. How do you graph to find linear mass density?

To graph to find linear mass density, you will need to plot the mass of the object on the y-axis and the length of the object on the x-axis. The slope of the resulting line will represent the linear mass density.

## 3. What are the units for linear mass density?

The units for linear mass density will depend on the units used for mass and length. However, some common units include kilograms per meter (kg/m) and grams per centimeter (g/cm).

## 4. Can linear mass density change for a single object?

No, linear mass density is a constant for a given object. It represents the distribution of mass along the length of the object, and this distribution does not change unless the object itself is altered.

## 5. How is linear mass density used to analyze waves?

Linear mass density is an important factor in determining the properties of waves, such as their speed and frequency. By understanding the linear mass density of a medium, we can better understand how waves will behave and interact with that medium.

• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
8
Views
823
• Introductory Physics Homework Help
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
44
Views
2K
• Introductory Physics Homework Help
Replies
26
Views
6K
• Introductory Physics Homework Help
Replies
13
Views
359
• Introductory Physics Homework Help
Replies
7
Views
696
• Introductory Physics Homework Help
Replies
22
Views
4K
• Introductory Physics Homework Help
Replies
59
Views
4K
• Introductory Physics Homework Help
Replies
30
Views
2K