Copy of lab 10 - waves

LAB 10 - Waves Traveling Waves (25 pts) 1. There is one long bungee cord strung out between two corners or walls in your lab room – make sure it is weighted down at one end and fastened securely at the other end. The tension in the string is just the weight of the large mass hanger and masses weighing it down. 2. Practice plucking the cord on one end, so that you generate a pulse that travels to the other end and then back again. This will happen several times, until the amplitude (height of wave) will die down. 3. Calculate and predict the speed of the wave pulse, using your knowledge of parameters that affect wave speed. There is sample bungee cord length near the front of the room in case you need to make measurements without taking down the long bungee cord. Show your calculation in your lab report. (10 pts) M = 2kg : 1kg from the plate and 1kg from the weight supporting to plate that’s hanging onto the cord 𝑉 = 𝑇 µ 0.03 µ = ? ? = .022 0.86 = 𝑉 = ?? µ = 2𝑘?(9.8) 0.03 = 25. 6 ?/𝑠 4. Design and perform an experiment to measure this speed. Note that if you will measure the time it takes for a pulse to get from one end of the string to another, you will make it easier (and reduce random uncertainty) by timing many pulses and dividing by the number of pulses – this is akin to measuring the thickness of a book page by measuring the thickness of the book and dividing by the number of pages. Detail your experiment in your lab report. (10 pts) 1) Measure the mass (in grams) of the mini cord 2) Put the mass on the bungee cord that is already attached to the wall 3) Stretch one end of the cord to the opposite wall so there is tension on the cord. 4) Flick the cord up and down and time how long it takes to complete 20 lengths 5) Then, measure how long the stretched cord is. 5. Discuss how your measured and predicted value compare; Write everything in your lab report. (5 pts)

The measured and predicted values are very close to each other. The difference in the values could be attributed to human error in calculating the time and energy loss, or other outside factors. 7.79s / 20 lengths = 0.39 s / length 10.5m / 0.39s = 26.92 m/s Standing Waves – String (25 pts) 1. On your lab table is a thin, relatively short bungee string, stretched between the Wave Oscillator and a pulley, over which is a mass providing tension. Although the end touching the wave oscillator oscillates (technically not a node), the amplitude is small enough for us to approximate that it is a node – it is basically fixed at both ends. 2. You will be using software called Function Generator (Desktop or Dock --> Lab Apps --> Function Generator). You can control the frequency with this, and the amplitude by adjusting the speaker Volume control (the speaker provides the signal). To adjust the frequency: you can either press the +/- buttons on the software, move the slider to the desired frequency, or enter the frequency with the keyboard directly. 3. After making all the necessary measurements, predict the frequencies at which you will see a standing wave (as in the top right illustration). Show all work in your lab report. (10 pts) Mass(string) = 4.92 g Hz ? 1 = ?𝑣 2? = ? 𝑇? ? 2(1?) = (1) (100?)(9.8?/𝑠 2 )(1?) 4.92? 2? = 7. 06 Hz ? 2 = ?𝑣 2? = ? 𝑇? ? 2(1?) = (2) (100?)(9.8?/𝑠 2 )(1?) 4.92? 2? = 14. 11 Hz ? 3 = ?𝑣 2? = ? 𝑇? ? 2(1?) = (3) (100?)(9.8?/𝑠 2 )(1?) 4.92? 2? = 21. 17 Hz ? 4 = ?𝑣 2? = ? 𝑇? ? 2(1?) = (4) (100?)(9.8?/𝑠 2 )(1?) 4.92? 2? = 28. 23 4. Perform the actual experiment – vary the frequency of the wave oscillator until you obtain standing waves, and make note of these frequencies. Record everything in the lab report. (10 pts)

The use of the end correction length does improve the agreement of your results to your predictions. Supporting calculations: f 1 =361 Hz f 2 =572.0 Hz f 3 =760.0 Hz f 4 =987.0 Hz f 5 =1170.0 Hz QUESTIONS (25 pts) 1. For the speed of the wave pulse, how close (within what %) were your experiment 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? (2 + 4 + 4 =10 pts) -Our group didn’t take into account the cord’s linear density because we used the unstretched string. We used the unstretched string so there is a larger theoretical value for velocity, which would make it faster. Percent error: (27.94 - 26.92) / 26.92 * 100 = 3.8% 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 calculation 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? (2 + 3 = 5 pts) -The quantities in our calculation for standing wave frequencies (the amplitude or height of the wave would decrease or get smaller as it oscillates less) would change by the addition of a small amount of weight to the mass hanger. If our standing wave goes away from this added mass, we would restore it by increasing the frequency. 2b. The point where the small bungee cord is moved up and down by the wave oscillator is approximately a node, even though there is slight vibration at that point. If you softly pinch one of the other nodes (except the node at the pulley) with your thumb and forefinger, explain why the wave still exists past that point. (5 pts) -The wave still exists past this point because at the node, the amplitude is zero. Therefore, if you softly pinch at one of the other nodes, it does not affect the amplitude of the “up and down” as it is already at zero. The preservation of the wave's existence beyond the pinched node underscores the fundamental principle that nodes are points of minimal amplitude. Therefore, the soft pinch, affecting an already zero amplitude, allows the wave to propagate undisturbed through the adjacent sections, contributing to the continuity of the wave pattern along the bungee cord.

3. If many frequencies are possible at the resonances with the sound tube, why is there the need for valves and stops in wind instruments? (5 pts) -If many frequencies are possible at the resonances with the sound tube, there’s still a need for valves and stops in wind instruments because for different notes, you need different wavelengths and frequencies to curate different sounds at different times. Different notes and musical phrases often require a precise combination of frequencies and wavelengths, which can be achieved by strategically manipulating the length of the air column through valves and stops. This ability to control the instrument's acoustics is essential for achieving the desired musical expression in a wide range of musical genres and compositions.