PC1141 Physics I. Speed of Sound

Transcription

1 Name: Date: PC1141 Physics I Speed of Sound 5 Laboratory Worksheet Part A: Resonant Frequencies of A Tube Length of the air tube (L): cm Room temperature (T ): C n Resonant Frequency f (Hz) Data Table 1: Closed tube. Question A-1: Derive a general expression for the ratio of each higher resonant frequency (f n where n > 1) to the lowest resonant frequency (f 1 ) for the closed tube. Show your work. Page 1 of 7

2 Speed of Sound Worksheet Page 2 of 7 Analysis A-1: For each resonance mode of the closed tube configuration, (1) determine the ratio of each resonant frequency to the lowest resonant frequency; and (2) compare each ratio to its theoretical value using percentage discrepancy respectively. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report. Analysis A-2: Perform a suitable linear least squares fit to your data: resonant frequency f and resonant wavelength λ so that the speed of sound can be determined. Plot a suitable linear graph for your data. Also show on the graph the straight line that was obtained by the linear least fit to the data as well as the error-bar of your data. Be sure to attach a copy of the graph (with the spreadsheet) to your laboratory report. Independent variable x: Dependent variable y: Gradient: ± (units) y-intercept: ± (units) Correlation coefficient: Analysis A-3: Estimate an experimental value for the speed of sound and its associated uncertainty with the appropriate number of significant figures. Show your work. Analysis A-4: What is the accuracy of your experimental determination of the speed of sound? State clearly the evidence for your answer.

3 Speed of Sound Worksheet Page 3 of 7 Diameter of the air tube (d): cm n Resonant Frequency f (Hz) Data Table 2: Open tube. Question A-2: Derive a general expression for the ratio of each higher resonant frequency (f n where n > 1) to the lowest resonant frequency (f 1 ) for the open tube. Show your work. Question A-3: Compare and contrast the series of ratios for closed and open tube configurations. Analysis A-5: For each resonance mode of the open tube configuration, (1) determine the ratio of each resonant frequency to the lowest resonant frequency; and (2) compare each ratio to its theoretical value using percentage discrepancy respectively. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report.

4 Speed of Sound Worksheet Page 4 of 7 Analysis A-6: For each resonant mode of the open tube configuration, determine its corresponding resonant wavelength. Perform a suitable linear least squares fit to your data: resonant frequency f and resonant wavelength λ so that the speed of sound can be determined. Plot a suitable linear graph for your data. Also show on the graph the straight line that was obtained by the linear least fit to the data as well as the error-bar of your data. Be sure to attach a copy of the graph (with the spreadsheet) to your laboratory report. Independent variable x: Dependent variable y: Gradient: ± (units) y-intercept: ± (units) Correlation coefficient: Analysis A-7: Estimate an experimental value for the speed of sound and its associated uncertainty with the appropriate number of significant figures. Show your work. Analysis A-8: What is the precision of your experimental determination of the speed of sound? State clearly the evidence for your answer.

5 Speed of Sound Worksheet Page 5 of 7 Part B: Standing Waves in A Tube Resonant frequency (f): Microphone positions Maxima Minima Hz Data Table 3: Sixth harmonic for the closed tube. Analysis B-1: Determine the resonant wavelength λ of the sound wave for the sixth harmonic in the closed tube with the corresponding uncertainty. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report. Experimental value: λ = ± (units) Analysis B-2: Estimate an experimental value for the speed of sound and its associated uncertainty with the appropriate number of significant figures. Compare it with the accepted value using percentage discrepancy. Show your work. % discrepancy = %

6 Speed of Sound Worksheet Page 6 of 7 Question B-1: Use the data that you have recorded, sketch the standing wave along the length of the resonance tube for the closed tube (sixth harmonic). Resonant frequency (f): Microphone positions Maxima Minima Hz Data Table 4: Eleventh harmonic for the open tube. Question B-2: Use the data that you have recorded, sketch the standing wave along the length of the resonance tube for the open tube (eleventh harmonic). Analysis B-3: Determine the resonant wavelength λ of the sound wave for the eleventh harmonic in the open tube with the corresponding uncertainty. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report. Experimental value: λ = ± (units)

7 Speed of Sound Worksheet Page 7 of 7 Analysis B-4: Estimate an experimental value for the speed of sound and its associated uncertainty with the appropriate number of significant figures. Compare it with the accepted value using percentage discrepancy. Show your work. % discrepancy = % 6 Laboratory Report Submit a laboratory report by ONE week after your laboratory session. Important: Before leaving the laboratory, have a demonstrator initial on your data table(s)! Last updated: Monday 20 th October, :02pm (KHCM)