Lab 9 Summary - Covers the \"Mechanical Waves\" lab PDF

Preview

Summary

Covers the "Mechanical Waves" lab...

Description

PHYS 215

30 November 2017

Mechanical Waves

Kristen Holmes

Oliver Larroque 16 November 2017

Holmes 1

PHYS 215

30 November 2017

Holmes 2

PURPOSE: The purpose of this experiment was to observe the properties of two types of waves, transverse waves in a string and sound waves in a tube. Using the measurable properties of frequency and wavelength, the velocity was determined for each type of wave. THEORY: In this experiment two procedures were performed. The first procedure involved adjusting the frequency of transverse waves in a string. The frequency(f) was adjusted to produce up to four nodes. For each adjustment, the wavelength(λ) was capable of being determined using the frequency at which the nodes were created and the distance between them. Using this data, the velocity of each wave was calculated. The second procedure was performed using a resonance tube to measure the position of each node located within it. For this procedure, the velocity of the sound waves were determined in two ways. The first involved knowing the temperature of the room and using this known information in a given equation. The second method was finding the wavelengths in accordance to the nodes located in the resonance tube. These waves that were observed during this experiment are examples of mechanical waves. Mechanical waves include water waves, sound waves, and seismic waves. This is why they are the most common type of wave that are encountered. Concepts of simple harmonic motion are often used to describe mechanical waves, because many of them are sourced by some sort of vibrating object. Mechanical waves are also governed by Newton's laws.

PHYS 215

30 November 2017

Holmes 3

Linear Density:

μ=m/L

μ=Linear Density m=Mass L=Length

Calculated Velocity:

V=√(T/μ)

V=Velocity T=Tension μ=Linear Density

Wavelength:

λ=2L

λ=Wavelength L=Length

Velocity of Wave:

V=λf

V=Velocity f=Frequency

PHYS 215

30 November 2017

Holmes 4

Standard Deviation:

σV=√{(xi-X)/n(n-1)}

σV=Standard Deviation of Velocity xi=Measured Value X=Average Value n=Number of Trials

Percent Error:

%Error=(│GAV-Mean│/GAV)(100%)

GAV=General Accepted Value Mean=Average Measured Value

Calculated Sound Velocity:

V=331m/s+.6T

V=Calculated Sound Velocity T=Temperature (℃)

PHYS 215

30 November 2017

Holmes 5

Wavelength of Sound Waves:

λ=2M

λ=Wavelength M=Slope

Velocity of Sound Waves:

V=λf

V=Velocity of Sound Waves λ=Wavelength f=Frequency PROCEDURE: The first measurement recorded for procedure one was the mass (m) and

length (L) of the string that was used in the experiment. Using these two measurements, the linear density was calculated (μ=m/L). The next measurement that was determined was used along with the linear density to find the calculated speed of the transverse wave (V=√(T/μ)). To find the tension (T) of the string, a 100kg mass was hung from another piece of string that was attached to a post holder. After recording these measurements procedure one was set up. A mechanical oscillator was placed on the post holder and the string was placed so that it passed through the fork of the oscillator. This oscillator supported no weight, its only purpose was to oscillate the string. To connect the oscillator to the computer, the banana plug patch cords that were connected to the Pasco 850 were plugged into the oscillator. The program used for this procedure was Capstone;

PHYS 215

30 November 2017

Holmes 6

this program was used to control the vibration of the oscillator, but not to collect any data. In Capstone the signal generator was chosen, then from the list 850 output 1 was selected. The waveform screen was set up for a sine wave, the amplitude was 4V, and the frequency was started at 20Hz. Now that the equipment and computer program are set up, the procedure was performed. The frequency was increased one hertz at a time until a single lobe was formed at maximum amplitude. A single lobe should display two nodes and one antinode. The frequency was recorded, and, using a meter stick, the distance (L) between the nodes of the vibrating string were measured and recorded. This distance was used to determine the wavelength of this wave (λ=2L). And the wavelength and frequency were used to determine the velocity of the wave (V=λf). The process of increasing the frequency and collecting the above data was repeated to find the velocity of a wave produced by a second harmonic (two lobes) and of a wave produced by a third harmonic (three lobes). Then, the average velocity was determined and the standard deviation was calculated. The average velocity was then compared to the calculated velocity of the transverse waves, found in the first part of this procedure, by calculating the percent error. The second procedure involves finding the velocity of the sound wave in two waves. For the first approach started with knowing the temperature (T) of the room that the procedure was performed in. This temperature was measured in Celsius. To find the calculated velocity of the sound wave, the equation V=331m/s+.6T was used.

PHYS 215

30 November 2017

Holmes 7

To set up the second procedure the banana cables were disconnected from the oscillator and connected to the resonance tube. The Signal Generator was set to 2.0V and the frequency was adjusted to 1200Hz. Starting the second procedure was done by pushing the plunger all the way into the resonance tube. Then, while listening for a increase in sound intensity, the plunger was slowly pulled outward. When the sound intensity noticeably increased, this means that t the length at which the plunger was located is resonance with the sound wave. The maximum intensity of the resonance was found carefully by making slight adjustments of the plunger. The location of maximum resonance was equal to the location of the antinode. The first position of maximum resonance indicates one node in the tube. This position was recorded along with the number of nodes present. The plunger was continuously pulled out until there was six positions recorded, indicating the presence of six nodes in the tube. Using the data collected, position and number of nodes, a graph of length vs. nodes was drawn. This graph provides the information needed to determine the slope of the line created. Then, using the slope (M), the wavelength could be determined (λ=2M). Knowing the frequency in the tube (1200Hz), this was used along with the wavelength to find the velocity of sound wave. This velocity was compared to the earlier calculated velocity of the sound wave by finding the percent error.

PHYS 215

30 November 2017

This is the apparatus used in procedure one and procedure two. Mechanical Oscillator: https://www.pasco.com/prodCatalog/SF/SF-9324_mechanical-wave-driver/ Resonance Tube: http://phylab.yonsei.ac.kr/board.php? board=emanual&sort=subject&indexorder=2&command=body&no=8

Holmes 8

PHYS 215

30 November 2017

Holmes 9

DATA: See attached data sheets. ANALYSIS: See attached work. CONCLUSION: Overall, this experiment produced results with very little error. Proving that by observing basic properties such as frequency and wavelength it is possible to determine accurate calculations for the velocity of mechanical waves. In many ways the two procedures that were performed are very similar, because the waves produced in each are both mechanical waves. This means that Newton's laws are applicable to both procedures. This can also explain why many of the calculations performed during the two procedures were similar. For procedure one, the standard deviation and the percent error were determined. The deviation calculated was very small (.66m/s). The percent error for procedure one was determined using the calculated velocity of the transverse wave (60.28m/s) as the General Accepted Value (GAV). The percent error of the average velocity (59.52 m/s) compared to the GAV was calculated to be only 1.26%. Small amounts of error could possibly come from not finding the most amplified lobe possible, therefore producing measurements that are slightly shy of what they should be. However, this procedure still proves to provide highly accurate measurements and results. Similarly, for procedure two the percent error was found using the calculated sound velocity as the GAV. The velocity determined from the data of the procedure (342.96 m/s) when compared to the GAV (344.67 m/s) produced a percent error of only .5%. There was an extremely small percent error in the procedure, which could possibly be a result of human error. It is possible to not be exactly precise in finding the location of the maximum resonance. This

PHYS 215

30 November 2017

Holmes 10

location is determined by sound, which could be different depending on the person performing the experiment.

PHYS 215

30 November 2017

Holmes 11

PHYS 215

30 November 2017

Holmes 12...