Ali J. Gangeh Phys 4C May 21, 2021 Lab 5: Acoustic Resonance and Beats Objective: The goal of this lab is to experiment on different frequencies and wavelengths to see if the interfere and distort each other. Equipment Used: - Phyphox app - Galaxy S8 phone - Lenovo desktop - Online tone generator Procedure: 1. Create a tube with the a4 papers and tape 2. Place the ruler onto the tube with rubber bands 3. Fill the bottle with water from tap 4. Measured room temperature with Maveric thermometer (25C) and used it to calculate the theoretical speed of sound 5. Placed my phone on top of the tube and used Phyphox app to play 1000Hz frequency sound. 6. I lifted the bottle as far as I could along the tube (leaving 8cm at top) I then slowly lowered it until I heard the most amount of sound. 7. I continued to do so until there was no more tube left and I recorded the distance from the top for each peak in volume 8. I repeated this for frequencies 2000Hz, 3000Hz, and 4000Hz 9. Then I used these measurements to find the experimental wavelengths for each frequency, subsequently finding the speed of sound. Data: Range of sounds I hear: 150-9000HZ Part 2 (Beats): All: One period: Expanded: Super expanded, fast modulation: Experimental results and analysis: In the second graph we see half the period of a slow modulation. The half period is: 255𝑚𝑠 − 60𝑚𝑠 = 195𝑚𝑠 A full period: 195𝑚𝑠 * 2 = 390 In the fourth graph we see the period of a fast modulation: 131. 4𝑚𝑠 − 130. 2𝑚𝑠 = 1. 2𝑚𝑠 Modeling beats: 𝑓𝑠𝑙𝑜𝑤 = 2. 564 1 𝑠 𝑓𝑠𝑙𝑜𝑤 = 833. 3 1 𝑠 ω𝑠𝑙𝑜𝑤 = 2 * π * 2. 564 = 1 2 (𝑤1 + 𝑤2) = 16. 11 1 𝑠 ω𝑓𝑎𝑠𝑡 = 2 * π * 833. 3 = 1 2 (𝑤1 − 𝑤2) = 5235. 8 1 𝑠 𝑤1 = 5235. 8 𝑤2 = 5219. 69 ω1 = ω2 = 𝑤1 2π 𝑤2 2π = 833. 30𝐻𝑧 = 830. 74𝐻𝑧 Conclusion and explanation of graphs: The first two graphs show the distortion of the wavelengths. We see that in some places the amplitude reaches almost zero as the two waves are interfering with each other, at other places it peaks as the sound waves overlap. The amplitude is related to how loud the wave is. Because of the distortion the amplitude of the sound wave changes over time. Once we zoom in we see the sound wave itself. That is what the two last graphs depict. If we were only playing a single frequency for the first two graphs we would see a blocklike structure but for the last two we would see waves of uniform amplitude. Through the graphs we were able to calculate the period of time it took for the slow waves caused by distortion as well as the short waves of the sound itself. Through this period we were able to recalculate our original frequencies. Our original frequencies were both about 20Hz higher than our calculated frequencies. We had a percent error of 2.27% for the smaller frequency and a error of 2.55% for the larger frequency. If I were to do this experiment again I would further minimize this error through working in a quieter environment so random noise wouldn’t effect my calculations.