Lamia.phys 226 02 - LAB PDF

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RESONANCE PHYS 226, LAB 2

Lamia Tasnim CONCORDIA UNIVERSITY | 40076908

resonance | Lamia Tasnim Introduction The objective of this experiment was to find the resonance frequency of an open-air cylindrical object (e.g., metal clothe hanging pipe) by using a tone generator on a recording device (phone) and try to find the speed of sound experimentally. By our theoretical knowledge, we know that “waves are capable of superimposing themselves, and when two sound waves of the same frequency align their peaks, the sound generates is much louder”. Sometimes, certain frequencies occur when a standing wave was created and has anti- nodes at the position. For which a resonance is created due to higher volume because of the peaks of the standing wave has higher amplitude then original sound wave. So, by using sound throughout this experiment it will give us a better and broader visualization and understanding of waves concept. Equation used throughout the experiment:

a.

b. Equation a is an idealized system to find the frequency (f) but for our scenario we will use equation b. Since we have to take account of the diameter of the cylinder (d) and length of the cylinder (L). The variable (v) is the speed of the sound in open air at 20o (343m/s) and (n) is the harmonic number. Our expectation from this lab is to get a positive linear trend on the resonance frequency graph due to equation a by respecting their harmonic number, the relationship of f and n is proportional.

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resonance | Lamia Tasnim Based on the taken measurements of the hollow cylinder length and diameter in table 1, the resonance frequency we expect is to be situated between the range of 2800- 7000 Hz. Results Length (L) Diameter (D)

Table 1 : measurments of aparatus. = 0.63 m = 0.041 m

Table 2: measurments of frequency from tone generator. n-values frequency (Hz) uncertainties 8.9 2290 ± 2E+02 12.6 3259 ± 2E+02 16.4 4256 ± 4E+02 21.3 5501 ± 2E+02 26.2 6779 ± 3E+02 Table 3: LINEST work of table 2 data. slope set(slope) r^2 F ss reg

258.75 0.00 1.00 1.39767E+32 12645114.00

± 3E-14 ± 3E-14 ± 3E-14 ± 3E-14 ± 3E-14

intercept set(intercept) set(y) df ss resid

0.00 0.00 0.00 3 0.00

± 5E-13 ± 5E-13 ± 5E-13 ± 5E-13 ± 5E-13

Table 4: experimental value for sound (m/s) 343 ± 4

! = V/(2(L+0.8d))*n v= f/n8(2(L+0.8d))*n

Graph 1: Different resonance frequencies vs n-values 8000 7000

Frequency (Hz)

6000 5000 4000 3000

y = 258.75x R² = 1

2000 1000 0 0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

n_values

frequency (Hz)

Linear (frequency (Hz))

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resonance | Lamia Tasnim Discussion The experimental value of the speed of the sound (v= 343m/s ± 4), table 4. is as equal to the theoretical value [v= 343 m/s] stated in the introduction along the margins of uncertainty. As we expected to have a positive linear trend to confirm the proportionality between frequency (f) and harmonic number (n) we see it in graph 1. The linear fit of the graph agrees with the data, where the resonance frequencies (table. 2) vary from lowest value of 2290 ± 2E2 to 6779 ±3E2 Hz. It doesn’t include the accepted value within the uncertainty range, but still could be supported since the discrepancy is slightly larger than uncertainty. The gradual increase in the plot of graph 1 is the proof of the proportional relationship found in equation b and this supports, and it is aligned with the theory of resonance. Experimental error sources could be led by the tone generator program. It is not a 100% accurate tool to be able to generate various frequencies, plus it was heard solely through phone speaker. Therefore, possibility of having interference of other sound frequency is highly likely. Furthermore, the accuracy of the measurement of the cylinder, length and diameter could be estimated ± 0.005m1. Since its impossible to get zero error source or perfect answer, errors could be reduced by measuring and using a greater precision, get an ideal and stable temperature for the speed. Conclusion To conclude, by finding the speed of sound we have gotten a better understanding on the concept of resonance and waves. We were able to find the experimental value (v= 343m/s ± 4) which agrees to our theoretical value [v= 343 m/s] more precisely and accurately by using the uncertainties.

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resonance | Lamia Tasnim References

A Guide to Uncertainties. (2020). Concordia University. Department of Physics. [accessed 2021 February 15th]. https://moodle.concordia.ca/moodle/pluginfile.php/4034787/mod_resource/ content/1/Uncertainties_guide.pdf

The Physics Classroom. 2021. Open-End Air Columns. Sound Waves and Music - Lesson 5 - Physics of Musical Instruments. https://www.physicsclassroom.com/class/sound/ Lesson5/Open-End-Air-Columns.

Harrison, David M. Error Analysis in Experimental Physical Science. University of Toronto, 31 July 2004, faraday.physics.utoronto.ca/PVB/Harrison/ErrorAnalysis/Accuracy.html.

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Shattuck, T. W. “Uncertainty Calculator.” Colby College Chemistry, www.colby.edu/chemistry/PChem/scripts/error.html?ModPagespeed=off.

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