Portland State University Standing Waves on A String Lab Report Link for the lab instructions:https://docs.google.com/document/d/e/2PACX-1vRhU_I4AWCxxQPVjZ

Portland State University Standing Waves on A String Lab Report Link for the lab instructions:https://docs.google.com/document/d/e/2PACX-1vRhU_I4AWCxxQPVjZBJlzfLGL97sMz68ohDS96LH9LqDYgKF3UNri59TQizGqbRRWFnPoVxCRqE4SpS/puba word document attached for the same instruction,requirements as in the instructed in the link/word doc.answering questions, objective included. Lab 1 – Standing Waves on a String
Objectives
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Identify a node or antinode of a wave
Explain the relationship between tension in a string and wave propagation velocity
Explain how to measure the wavelength
Calculate wave velocity given the tension, wavelength and mass per unit length of the string
Writeup Requirements
Overview – 4 pts, Data & Analysis – 6 pts, Questions – 8 pts, Lab 1 Survey – 2 pts
Preparation
Watch the lab lecture video here.
Watch the lab demo video here.
1. In the lecture video, we discuss how waves propagate. For ocean waves, do the water molecules
themselves move with the same velocity as the wave velocity?
2. From the lab video, what resonant frequency was found for the n = 2 case with 200 g of mass on the
string?
Many common musical instruments are string instruments (pianos, violins, guitars, etc.). The vibration of a string
causes a note that may be tuned by adjusting the tension on the string. The vibration is in the form of a standing
wave that may be considered as the superposition of two waves of the same frequency traveling in opposite
directions. The phases of the forward and backward waves cause a cancellation of the waves, or node, every half
wavelength (where string displacement is minimum) and a peak between the nodes (antinodes where string
displacement is maximum). Figure 1-1 shows the location of nodes and antinodes for a standing wave with two
antinodes.
Figure 1-1. Plot of a standing wave with three nodes, and two antinodes.
The propagation velocity of the wave v (m/s), depends upon the linear mass density μ (kg/m), of the string and
upon the tension FT (N), in the string according to the equation
(11)
We are not always able to measure the velocity of a propagating wave directly, therefore we find it by its
relationship to the frequency f (Hz, or cycles/s), and wavelength λ (m),
(1-2)
3. What are two variables that determine the fundamental frequency of a guitar string?
4. A violin string produces the musical note A, which has a frequency of 440 Hz. The string has a linear mass
density of 7.8 x 10-4 kg/m. If the wavelength for the standing wave pattern is 65 cm, find the tension FT on
the string.
5. If the thickness of the string were increased, how would that change the propagation speed of the
traveling wave? On an instrument, how would this change the frequency, or pitch for the same standing
wave pattern?
Standing Waves on a String
Follow the link below to the Geogebra website where a simulation experiment of standing waves on a string can
be found: https://www.geogebra.org/m/qYX5eakP
Figure 1-2. Front panel of Standing wave on a string simulation from Geogebra website. The string is hung between
a tuning fork oscillator, and connected on the opposite end to a pulley for setting the tension. The overall
length L between the oscillator and pulley is set at 4.0 m.
1. First select a linear mass density for the simulated string. To do this, make a selection using the slider at
the bottom of the simulation labeled ‘Linear Density”. (hint: you may want to use a linear density value
near 1 x 10-3 kg/m). We will later verify this value through our simulated experiment.
2. Drag the ‘Tension’ slider until it reads approximately 20 N, this is equivalent to placing a 20 N force at the
left end of the string (fine adjustments in the value can be made by using the arrows on a keyboard).
3. Start with the Frequency slider all the way to the left at 45 Hz.
4. Slowly adjust the ‘Vibration Frequency’ slider by dragging it to the right until a standing wave is visible on
the string.
The wave velocity will be fixed by the dimensions of the string, and weight placed on the end to set the tension.
Thus the product of the wavelength and the frequency will be a constant value. To achieve a standing wave, you
will adjust the ‘vibration frequency’ slider until the corresponding wavelength has nodes where the string is tied
off. The string will show the largest vibrations when you achieve a standing wave (see Figure 1-1).
5. Record your value for the tension applied to one end of the string in a data table similar to Table 1-1.
6. Ensure a standing wave pattern is still visible in the simulation (if not adjust the Vibration frequency until
one appears). Note the total number of peaks (antinodes) and record it in your data table.
7. Determine the wavelength of the standing wave generated on the string by counting the number of
antinodes N, and calculating it into Eq. (1-3)
(1-3)
8. Record the measured wavelength and the vibration frequency in your data table.
9. Increase the frequency until you achieve a different standing wave pattern that has one more
node/antinode than the previously observed standing wave. Record the values as you did previously until
the data table is completely filled out. Calculate the velocity from equation (1-2).
Note: for some combinations of linear mass density and tension, you may have the vibration frequency range to fill
out all rows of the table. In these cases complete the table for as many numbers of antinodes as you can.
10. Calculate the average and standard deviation of your velocity values, and record them in your table.
Table 1-1. Example data table for observed standing waves on a string.
Total number of antinodes
Frequency f (Hz)
Wavelength λ (m)
Tension (N):
Velocity v (m/s)
Average Velocity v (m/s):
Standard Deviation:
11. Repeat previous steps for tension values near 40 N, 60 N, and 80 N.
12. Plot the average velocity squared versus the tension (v2 vs. FT).
13. Include a best fit line, and have the equation displayed on the graph. The results should show a straight
line as predicted by Eq. (1-1).
14. Calculate the linear mass density, μ, of the string from the slope of your graph.
6. What will happen to the standing wave if we increase the tension applied to the string while leaving the
vibration frequency the same?
7. How do these two values for linear mass density (one from slope, and one from simulation settings)
compare based on a percent difference calculation?
8. Why is it better to calculate the mass density from the slope rather from individual data points?
Complete the Post Lab 1 Survey on D2L once you have
submitted your report. This is located in the Quizzes section.

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