LabReport13 - PHY121

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CUNY College of Staten Island *

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121

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Chemistry

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May 23, 2024

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docx

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SPEED OF SOUND - RESONANCE TUBE METHOD Course: PHY 121 Section: 18296 Student Name: Javier Santos Lab Partner: Alexis Sander Instructor: Siyka Shopova Experiment Performed: 05/08/2023 Report Written: 05/14/2023

Objectives The objective of this lab report is to determine the wavelengths in air of sound waves of different frequencies by the method of resonance in a closed-end pipe, through this we will be finding the speed of sound. Physical Principles The speed of sound can be measured directly by timing the passage of a sound over a long, known distance. To do this with an ordinary watch requires a much longer distance than is available in the laboratory. For all waves the following relationship holds: When a tuning fork is vibrating near the open end of a tube closed at the other end, a strong reinforcement of the tuning fork sound will be heard if the air column in the tube is the right length. This reinforcement is known as resonance. To find the length of the air column which produces resonance for a given tuning fork, it is necessary to vary the length of the tube. An acrylic tube is inserted inside the 1000 ml graduated cylinder. The cylinder is then filled with water being careful not to spill. The tuning fork is struck on a soft rubber wedge. While the fork is vibrating it is placed above the graduated cylinder , then the tube is raised to change the length of the air column in the tube until the sound intensity is at a maximum. Since the shortest tube length for which resonance occurs is L=λ/4, it follows that λ=4L. Practically, this relationship must be corrected for the diameter d of the tube. This gives: (Eq.1) Going back to Eq. 1, since we are first finding speed of sound based on resonance we will redefine Eq. 1 as vR. Therefore, (Eq.2)

At 0°C the speed of sound is 331 m/s. The formula for speed of sound when taking into account temperature, T (in degrees Celsius), is as follows: (Eq.3) Apparatus used in this Experiment • Metric ruler or Vernier caliper • Tuning fork activator (soft rubber wedge) • Tuning forks: 384 Hz, 440Hz, 512 Hz and 1024 Hz • Acrylic tube with cm scale • 1000 ml graduated cylinder with water Procedure First step we did on the procedure was to ready the needed equipment for the experiment, including our notebooks to write our collected data. First procedure we did was to record the room temperature as shown on the teacher’s table. I recorded 21.1 degrees celsius. After that I measured and recorded the inner diameter of the hollow tube in meters, which was 0.034m. Once I got my data, me and my partner inserted the acrylic tube inside the graduated cylinder. Once everything was setted up, we began our data collection. The first tuning fork we measured was the 1024 Hz one and after striking it, I slowly raised the inner tube until we heard a strong resonance. We measured 7 cm for the 1024 Hz tuning fork. We did the same procedure through the remaining tuning forks and collected our data. We then used the formula Vr and compared it to the known speed of sound. Calculations

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Data Collected and known values from the experiment: Room Temperature = 21.1 ° C Diameter of the hollow tube = 0.034m Vt was calculated using the formula shown on Eq.3: V T = 331.5 m / s +( 0.6 m / s ⋅ °C ) T Solving the Speed of Sound using the known Temperature: V T = 331.5 m / s +( 0.6 m / s ⋅ °C ) T V T = 331.5 m / s +( 0.6 m / s ⋅ 21.1 ) T V T = 344.16 m / s Vr was calculated using the formula shown on Eq.1 and Eq.2: λ = 4 ( L + 0.3 d ) V R = λ f Solving the Vr using the 1024 Hz tuning fork: λ = 4 ( L + 0.3 d ) λ = 4 (( 0.07 m )+ 0.3 ( 0.034 )) λ = 0.3208 m

V R =( 0.3208 )( 1024 ) V R = 328.5 m / s Solving average Vr: V Rave = 328.5 + 328.08 + 325.95 + 330 5 V Rave = 328.25 m / s % Error = ¿ known value − experimental value ∨ ¿ known value ⋅ 100% ¿ % Error = ¿ 344.16 − 328.25 ∨ ¿ 344.16 ⋅ 100% ¿ % Error = 4% Discussion The experiment aimed to determine the speed of sound in air using the resonance tube method. These values can be compared with the theoretical speed of sound in air, which is approximately 344.16 m/s at our given room temperature. In the first trial, the calculated speed of sound was measured to be 328.5 m/s. After experimenting with the same procedure, we got an average Vr of 328.25, which

proves that our experiment was successful after calculating our percent difference, which is only 4%. But if students and professors were not satisfied with the result, the best way to improve the accuracy of the results, several measures can be taken. Using more precise instruments, such as a Vernier caliper, to measure the length of the air column can reduce measurement errors. Ensuring the resonance tube is tightly sealed and the water level is accurately adjusted can help minimize unwanted interference. Conducting the experiment in a controlled environment with known temperature and pressure conditions can also enhance the accuracy of the measurements. Conclusion The speed of sound in air was successfully determined using the resonance tube method, and the experiment yielded highly accurate results with a low percentage difference compared to the known speed of sound value. The theoretical speed of sound in air is approximately 343 m/s at room temperature. The low percentage difference between the measured speed of sound and the known value indicates the effectiveness of the resonance tube method and the soundness of the experimental procedures. These results validate the fundamental principles of wave propagation and the ability to measure the speed of sound using the resonance tube method. In conclusion, the resonance tube method proved to be a reliable and effective technique for determining the speed of sound in air. The experiment's success, demonstrated by the low percentage difference between the measured and known speed of sound values, highlights the importance of precise measurements, controlled experimental conditions, and a thorough understanding of acoustic principles. Further studies can build upon these findings and explore the speed of

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