YAMBAO, Monn Juleuse F.
[email protected]
E303: Transverse Wave: Frequency of Vibration
METHODOLOGY
Two experiments were done last time due to some circumstances that made the class to lack time and to be late compared to the official class syllabus. The students were able to accomplished the job by equally dividing the time into two. The first experiment was about Kundt’s tube; as soon as the first experiment was conducted, the set up for the transverse wave experiment was immediately done. Transverse waves assume a sinusoidal wave pattern and visually represented by a standing wave. This is due to the superposition of the two travelling waves which is known as incident and reflected waves. This experiment is divided into two parts. For the first part of the experiment, the students were required to determine the frequency of vibration with a constant linear mass density. The students were gave the liberty to select any size of the guitar string. After selecting a guitar string, it's end was tied to the stylus of the string vibrator (See Figure 1) and it was passed over a pulley (See Figure 2).
Figure 1: End of a guitar string tied to the stylus of the string vibrator
Figure 2: Guitar string passed over a pulley
At the end of the guitar string, a mass hanger was attached. A mass was added on the mass hanger (See Figure 3) and the frequency knob was adjusted to 114 Hz (See Figure 4).
Figure 3: A mass with a mass hanger at the other end of the guitar string.
Figure 4: A frequency knob adjusted to 114Hz After doing so, the amplitude knob was slowly adjust to make certain that the segment formation is clearly defined to be seen. The number of distinct of segment formation was counted and it's length was also measured (See
Figure 5).
Figure 5: A clearly defined line segment being measured
To minimize error, the segment near the stylus was not considered. All data were recorded and the experimental value for the frequency of vibration was solved using the equation below.
√
The whole procedure were repeated with each trial with increasing mass added to the hanger. The average experimental value of frequency of vibration was computed and the percentage was solved right after. For the second part of the experiment, the students were required to determined the frequency of vibration with variable linear mass density. Same procedure was used but this time different sizes of guitar strings were used for each trials. The tension for this experiment was held constant for all trials. Same equation was used to solved for the frequency of equation.
Diagram:
1. Sine Generator - electronic equipment that generates a pure, oscillating frequency in sinusoidal pattern to the string.
2. String Vibrator - drives a string to produce standing wave.
3. Set of Weights - were used to vary the tension
4. Pulley - used with a string to lift weight 5. Mass Hanger - is where the weight was
placed
6. Stylus - a small metal that produces sound when touches to the vibrating string; is where the string is attached 7. Guitar Strings - used as the medium
DATA AND RESULTS
The tabulated form of all the data gathered by conducting the experiment were shown below:
Table 1: DETERMINING THE FREQUENCY OF VIBRATION (constant linear mass density) Diameter of wire: 0.014 in Linear Mass Density of Wire (µ) Trial Tension T (dynes) Number of Segments N Length of String Frequency of Vibration (Hz) 0.0078 1 102900 2 33 110.064293 0.0078 2 73500 2 28 109.632252 0.0078 3 122500 2 36 110.082489 0.0078 4 83300 2 30 108.931616 0.0078 5 132300 2 36 114.401079 Average Frequency of Vibration 110.622346
Actual Value of Frequency of Vibration 114
Percentage Error 2.962855%
Table 1 shows that the Tension is directly proportional to the Length of the String and the Frequency of Vibration. This means that as the Tension increases, the length of the string and the frequency of vibration also increases. However, some inconsistencies can be seen on the table. This inconsistencies are due to some errors in gathering the data. This explains the percentage error that was obtained.
Table 2: DETERMINING THE FREQUENCY OF VIBRATION (variable linear mass density)
Trial Diameter Of Wire Linear Mass Density of Wire (µ) Tension T (dynes) Number of Segments N Length of String Frequency of Vibration (Hz) 1 0.010 0.0039 102900 2 44 116.740 2 0.014 0.0078 102900 2 33 110.064 3 0.017 0.0112 102900 2 26 116.580 4 0.020 0.015 102900 3 36 109.132 5 0.022 0.0184 102900 4 44 107.492 Average Frequency of Vibration 112.002
Actual Value of Frequency of Vibration 114
Percentage Error 1.753%
Table 2 shows that the linear mass density is somehow proportional with the number of segments and inversely proportional with the frequency of vibration. As the linear mass density increases, the number of segments also increases while the frequency of the vibration decreases. These relationships can be verified through theoretical analysis. However, some inconsistencies can be seen on the table. Such inconsistencies are due to some errors in gathering the data. This explains the percentage error that was obtained.
SAMPLE COMPUTATION
The method that was used in computing the experimental value of the frequency of vibration is shown below:
Part A: Determining the Frequency of Vibration with
Constant Linear Mass Density
Given:
√ ( ) √ | ( ) | | | 2.96%
Part B: Determining the Frequency of Vibration with
Constant Linear Mass Density
Given:
Solution:
√ ( ) √ | ( ) | | | 1.75%DISCUSSION
Among the experiment done, I can say that this is the most amusing, amazing, cool and interesting experiment so far. The devices used were very scientific and high technology compared to the Kundt’s tube experiment which is very primitive. It also involved simple computations. The values obtained through conducting the experiment are directly substituted on the formula given in order to obtain the experimental value of the frequency of vibration. We are able to enjoy the activity and because of that we are able to finish our work ahead of other groups. However we did encounter some problems since somehow we did not understand how the equation works. At first we didn't multiple the length of the segment to the number of segment, we thought that there is something wrong with the equation until we asked for the other group's help. Gladly, we didn't encounter any problem with regards to the set up and procedure of the activity. We did obtain great values for the percentage error which makes me say that we did a really good job.
For the first part of the experiment, we were able to get a percentage error of 2.96%. The value is pretty much lower than the percentage error that was obtained in the previous experiments. The reason behind this must be that the temperature is not considered in this experiment. The diameter used in the first part of the experiment was 0.014 cm which has an equivalent value of the linear mass density which is
. As it has mentioned on the data and results, the tension is directly proportional to the length of the string and the frequency of vibration. Yet, some inconsistencies on this proportionality could be seen on the first table. These inconsistencies is one of the very reason of the percentage error obtained. As shown on table 1, the group have obtained a consistent number of segments. The possible reason on this consistency is the string used. The group have used only one size of the string.
for the second part of the experiment, the percentage error obtained was a bit lower than the one obtained in the first part. The tension was held constant in this part while the Linear mass density varied. The relationship of the factors that affects the frequency of vibration are can be seen on the data and results. The data in table 2 that was gathered and computed by the
students is matched on the theory of frequency of vibration.
CONCLUSION
The objectives of the experiment is to determine the frequency of vibration of a stretched string and to study how the frequency of vibrating string is affected by tension and linear mass density.
By conducting the experiment the students were able to conclude that the theory regarding the transverse wave are true. These are waves which occur when the particles of the medium vibrate perpendicularly to the direction of the wave propagation. From the results obtained through the experimentation we can demonstrate the relationship of tension and linear mass density to the frequency of the vibrating string. As can be seen on the first part, it can be concluded that the tension is directly proportional to the length of the string and the frequency of vibration. And preferring to the second part, it can be concluded that the linear mass density is directly proportional with the number of segments and inversely proportional with the frequency of vibration.
Finally, the students were able to accomplish the given objectives of the experiment.
ACKNOWLEDGMENT
First of all, I want to thank our Almighty God for without Him all of this are not possible.
I gratefully acknowledge the important contributions and guidance provided by the following members of Group 5:
Joren Angeles, for the computations and listing of records of the experiment.
Eleazar Carlo Parazo, for the setup and photo records of the experiment.
James Ramirez, for performing and maintaining the cleanliness of the experiment
Emil Salazar, for performing and for the laughter.
John Yambing, for the computations and for his MS Excel expertise.
Lastly, I would love to express my gratitude to our hardworking Professor, Mr. Ricardo De Leon, who guided us and gave us encouragement on times of problems.
REFERENCES
[1] R.A. Serway and J.W. Jewett, Physics for Scientists and Engineers, 6th Ed. (Thomson, Belmont, CA, 2004), pp. 100-102 [2] Beiser, Arthur, Concepts of Modern Physicss,
5th Ed., McGraw-Hill, 1995
[3] Halliday and Resnick, Fundamentals of Physics, 9th Ed., Wiley 2011
[4] Laboratory manual, General Physics 3, Department of Physics, Mapúa Institute of Technology
[5] Padua, A., Practical and Explorational Physics, 2003