205_sec 26_Lab 10_Sankeshwarkar, Nath, Garcia

LAB 10: WAVES —------------------------------------------------------------------------------------------------------------------ Traveling Waves: 3. Calculate and predict the speed of the wave pulse. Show your calculation. V = √(T ) /? T = (2 kg) (9.8 m/s 2 ) = 19.6 W = m/L = (24.79 x 10 ? -3 kg)/(0.81 m) = 0.03060494 kg/m V = √(T ) = √((19.6)/(0.03060494)) = V = 25.31 m/s /? 4. Design and perform an experiment to measure this speed. measurement => V = s/t V = (0.23*43*10)/3.55 V = 27.9 m/s —------------------------------------------------------------------------------------------------------------------ Standing Waves – String: Predict the frequencies at which you will see a standing wave: = (2L)/n ? F n = (v ) = (v/2L)/n /? V = √(Tstring string) /? Tstring = 0.1 kg string = (5.2 x 10^-3 kg)/(1.73 m) = 3.006 x 10 ^-3 ? V = 33.3 m/s F n = [(v) / (2L)] (n) F 1 = [(33.3) / (2)(1)] (1) = 16.65Hz F 2 = [(33.3) / (2)(1)] (2) = 33.3Hz F 3 = [(33.3) / (2)(1)] (3) = 49.95 Hz Perform experiment and record everything. n = 2: 21 Hz n = 1: 10 Hz n = 3: 32 Hz —------------------------------------------------------------------------------------------------------------------ Standing Waves – Tube: Prediction: F n = (v s /2L’)n

L’ = 0.76 + 0.6(0.075) L’ = 0.805 m F n = [(340)/(2*0.805)](n) F 1 = 211.18 Hz F 2 = 422.36 Hz F 3 = 633.54 Hz Perform experiment and record everything. Experimental frequency at F 2 = 430.9 Hz Does the use of the end correction length improve the agreement of your results to your predictions? Give supporting calculations with answer. With end correction: F 2 = 422.36 Hz Without end correction: F 2 = [(340)/(2*0.76)](2) = 447.37 Hz 447.37 - 430.9 = 16.47 Hz 430.9 - 422.36 = 8.54 Hz The experimental frequency we got was 430.9 Hz. This is closer to the experimental frequency, therefore, the end correction length does improve the agreement to the results compared to the predictions. —------------------------------------------------------------------------------------------------------------------ QUESTIONS: 1. For the speed of the wave pulse, How close (within what %) were your experimental to your predicted results? Did you take into account that the cord’s linear density changes when there is tension in it? How would that affect the predicted speed of the speed of the wave pulse — would that make it slower or faster? - (10-16.65)/16.65 → 40% error for n-1. - We did not take into account the cord’s linear density when there is tension in it. The linear density would make the wave pulse slower. 2a. With the small bungee cords driven by the wave oscillator, suppose you get a standing wave at a particular frequency and mass hanger mass — what quantities in your calculations for standing wave frequencies would change by the addition of a small amount of weight to the mass hanger? If your standing wave goes away from this added mass, how would you restore it? - If there was an additional amount of weight added to the mass hanger, the tension would increase, which would increase velocity as well as frequency. If the standing wave goes away, I would just increase the frequency being produced.