Purpose: In this lab, we will be doing 3 major things: 1) Collecting and organizing data to obtain resonant points in a closed pipe, 2) measure the length of a closed-pipe resonator, and 3) analyze the data to determine the speed of sound. Procedure: 1. Fill the graduated cylinder nearly to the top with water, with a tall glass tube open at both ends (the water level with act as the closed end). 2. Determine the room’s air temperature, and also measure the diameter of the glass tube.

Record the data.

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Select a tuning fork and record the frequency (in Hz) in the data table. Record the data. 4. Strike the tuning fork against a rubber stopper, and hold it just above the opening of the glass tube. Raise or lower the glass tube/fork until the loudest sound is heard. 5. Once you hear the loudest resonation, hold the tube in place. Measure the distance from the water level, to the top of the glass tube. Record the data. 6. Repeat Steps 3-5. Calculations/Analyze (Taken from Trial #1): 1.

Accepted Speed of Sound = 331 m/s + 0. 6(Temperature) v = 331 + 0. 6(22) = 344. 2 m/s 2. Wavelength = 4 x Length of Tube above Water ? = 4 x (0. 32) = 1. 28 m 3. Experimental Speed of Sound = Frequency x Wavelength v = 256 x 1. 28 = 327. 68 m/s 4. Accepted Value – Experimental Value x 100 = Percentage Error Accepted Value 344. 2 – 327. 68 x 100 = 4. 9 % 344. 2 5. Corrected Wavelength = 4(L + 0. 4d) ? = 4(0. 32 + 0. 4(0. 031)) = 1. 3296 m 6. Corrected Speed of Sound = Frequency x Wavelength v = 256 x 1. 296 = 340. 38 m/s 7. Accepted Value – Experimental Value x 100 = Percentage Error Accepted Value 344. 2 – 340. 38 x 100 = 1. 11 % 344. 2 Data: Accepted Speed of Sound = 344. 2 m/s Temperature = 22° C Trial |Tuning Fork Frequency (Hz) |Length of Tube (m) |Wavelength (m) |Speed of Sound (m/s) |Corrected Wavelength (m) |C

orrected Speed of Sound (m/s) |Relative Error (%) |Corrected Relative Error (%) | |1 |256 |0. 32 |1. 28 |327. 68 |1. 3296 |340. 38 |4. 8 |1. 11 | |2 |293. 7 |0. 235 |0. 94 |276. 08 |0. 9896 |290. 5 |19. 9 |15. 56 | |3 |394 |0. 193 |0. 772 |304. 17 |0. 8216 |323. 71 |11. 63 |5. 95 | | Diameter = 0. 031 m Conclusion/Going Further/Real-World Physics: In this experiment, we were resulting to a few conclusions, but ultimately trying to determine resonant points in open-closed pipes, and use these points to find an experimental speed of sound (which averages to about 302. 64 m/s or the corrected 318. 25 m/s). These averages we determined from the trials can be compared to the accepted speed of sound (344. m/s in this specific temperature), and we determine the relative error percentages: 344. 2 – 302. 64 x 100 = 12. 07%344. 2 – 318. 25 x 100 = 7. 54% 344. 2 344. 2 These sources of error come from a few specific things: • Human Error: Inaccurately measuring the tube, minor calculator errors, misreading the room thermometer, mishearing resonance • Mechanical Error: Inaccurate equipment Going Further: Of the trials we did, Trial #1 proved to be the most accurate speed of sound (the 256 Hz tuning fork).

We can say this because it had the lowest percentage of error. Real-World Physics: Resonant frequencies and the size of organ pipes, shown in this lab, are very closely related, and the relationship between the two can actually be found by the following derivation: wavelength is equal to 4 times the length of the pip (? = 4L). Wavelength is also equal to velocity divided by frequency (? = v/f), and therefore is equal to the previous equation (v/f = 4L ( f = v/4L, the open-close equation for frequency).

This means for pipes, the longer the pipe, the smaller the frequency, and shorter pipes at higher frequencies. Questions/Conclude and Apply: 1. The next two lengths where the resonance will occur would be at the wavelength being double the length, or 4 times the length. 2. Yes, by extending the length of the pipe, one could find another position where resonance occurs by going to the next octave (8 musical steps away). Partner: Rosa Lee Florence