Lab 2_ Speed of Sound- Resonance Tube

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Lab 2: Speed of Sound- Resonance Tube Written by: Quinn Jones and Boluwatife Ade-Okanlami Due: February 6, 2024

Objectives: ● Determine the effective length of a closed tube at which resonance occurs for several tuning forks. ● Determine the wavelength of the standing wave from the effective length of the resonance tube for each tuning fork. ● Determine the speed of sound from the measured wavelengths and known tuning fork frequencies and compare with the accepted value. Equipment List: ● Resonance Tubes ● Tuning forks (500 to 1040HZ) ● Rubber hammer ● Thermometer Experimental Procedure: 1. Find the temperature of the air in the room and record it in Table 1 2. Adjust the water level to at least 5.0cm = 0.050m 3. Strick a tuning fork with a rubber hammer. Keep the fork vibrating continuously with a large amplitude. While the tuning fork is vibrating, another person slowly lowers the water from the top while listening for resonance. Measure the position of each resonance to the nearest millimeter. Do this three times and record the values in Data Table 2. 4. Repeat step 3 to locate as many other resonances and record the values in Data Table 2 5. Use a second tuning fork of a different frequency. Repeat steps 1-4 and record in Data Table 3. 6. Use Equation 5 to calculate the accepted value of the speed of sound from the measured temperature and record it in Data Table 1. 7. Calculate the mean and standard error of the three trials for the location of each of the resonances and record the answers in Data and Calculations Tables 2 and 3. 8. Use Equation 4 to calculate the appropriate wavelengths. With three resonances recorded 2 values can be determined. Use mean values of the lengths to calculate the wavelengths. 9. Calculate the mean and standard error of the number of independent wavelengths measured for each tuning fork and record the values in the Calculations Tables.

10. From the values and the known values of the tuning fork frequencies, calculate the experimental value for V , the speed of sound 11. Calculate the percentage error of the experimental values of V compared to the accepted value of the speed of sound in the Data and Calculations Table Data and Calculations Table 1: Room Temperature = 26 ℃ Speed of sound = 343m/s Data Table 2: Frequency Fork One = 512 L1(cm) L2(cm) L3(cm) 15.4 49.2 68.1 15.5 49.3 72.0 15.6 48.9 69.2 L1(m) L2(m) L3(m) 0.154 0.492 0.681 0.155 0.493 0.720 0.156 0.489 0.692

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Data Table 3: Frequency Fork Two = 1024 L1(cm) L2(cm) L3(cm) 7.1 24.2 42.1 8.0 24.5 41.3 8.2 24.6 42.3 L1(m) L2(m) L3(m) 0.071 0.242 0.421 0.080 0.245 0.413 0.082 0.246 0.423 Calculations Table 2: Mean L1 = 0.155m Mean L2 = 0.491m Mean L3 =0.698 m ∝ L1 = 0.003m ∝ L2 = 0.001m ∝ L3 = 0.009m λ1 = 2(L2-L1) = 0.672 λ2 = (L3-L1) = 0.207 Meanλ = 0.440m ∝ λ = 0.164m V=fMeanλ= 225.28 m/s % err = 16.4%

Calculations Table 3: Mean L1 = 0.078m Mean L2 = 0.244m Mean L3 = 0.419m ∝ L1 = 0.003m ∝ L2 = 0.001m ∝ L3 = 0.002m λ1 = 2(L2-L1) = 0.332 λ2 = (L3-L1) = 0.175 Meanλ = 0.254m ∝ λ =0.0785 m V=fMeanλ= 269.m/s % err = 0.785% Sample Calculations: Mean L1= 0.154 + 0.155 + 0.156/3 = 0.155 λ1 = 2(L2-L1)= 2(0.491-0.155) = 0.672 Questions: 1) We believe each of our measurements is accurate because all of the trial results we contained are close to each other in value and when we calculated the standard error we got an average of 0.2%, indicating that our trial mean did not deviate far from the true population mean. 2) An indication that the trials that we conducted are precise is that our standard deviation of L1, L2, and L3 have an average of 0.003. 3) With the mean value of our wavelength being λ = 0.254 the new values of L for the second tuning fork would calculate to be L1=0.0635m L2=0.1905m and L3=0.3175m. For the first tuning fork, the new L values would be calculated to L1=0.11m, L2=0.33m, and L3=0.55m. Comparing the original and new values of L for the tuning fork, it can be seen that the newly calculated value of L is slightly higher than the original values which was to be expected, The standard error for the new L values is calculated to be 0.103 which is 9.8% higher than what was calculated for the original values indicating that newly calculated value may not be as accurate. For

the second tuning fork, the new values are also higher than the original values with the standard error of the new values being 0.039 which indicates that the values are slightly accurate but not as accurate as the original values. 4) From the formula given, we can see that the speed of sound is directly proportional to the square root of temperature. So if the temperature increases by 10°C, we can estimate the change in the speed of sound using the formula and then use this change to estimate the change in ( L2 - L1 ) for each tuning fork. If the speed of sound increases due to the temperature rise ( L2 - L1 ) would be smaller at the higher temperature. Also if the speed of sound decreases due to the temperature rise, it would be larger at the higher temperature. 5)

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