Lab Exercise
![[url=https://remote.rsccd.edu/en/liturgical-organ-pipe-organ-reeds-811168/,DanaInfo=pixabay.com,SSL+]"Organ"[/url] by Sebastiano_Rizzardo is in the [url=https://remote.rsccd.edu/publicdomain/zero/1.0/,DanaInfo=creativecommons.org+]Public Domain, CC0[/url]](https://www.geogebra.org/resource/H5cMFt4p/QVqHsy7CbqQt75AM/material-H5cMFt4p.png)
Guitar String Resonances
In this section you will measure the resonant frequencies of waves formed along a guitar string. Do not confuse these with sound in air. A string will have traveling waves traveling both ways along its length once plucked. These will form a series of resonant standing waves on the string. These standing waves will stir up the air which will in turn excite resonances inside the body of the guitar (which will be of the same frequencies), but the origin of all that was the standing waves on the string. We will use a sound sensor obtained from this link to see the sound graphically in real time: Spectral Analysis Software.
1. Get the software installed and running. On the right side of the lower window, change the scaling to 4x. Also un-check the logarithmic x-axis.
2. Pluck a single guitar string close to your mic input on your laptop. If you don't know where it is, move the guitar around your laptop while it's making sound until you see the signal grow on the screen. That should help you locate the mic input.
3. Just after the string is plucked near your mic, hit "Save Spectrum". This will open another window. Go to view, and remove the check mark before "phase". Max out the window and click and drag to zoom into the region between 0 and 2000 Hz. Make sure what you recorded contains at least 7 clear harmonics. If not, redo this part.
4. Record the values of the first 7 harmonics of the string. You can see the values as you move the cursor around the plot. Take note that sometimes these harmonics will have near zero amplitude. From theory you should know what to expect in terms of their frequencies. This often helps discerning what is noise versus signal.
5. Plot the frequency (y-axis) versus the harmonic number n (x-axis) in whatever software you wish.
6. Create a linear fit to the data with the equation displayed. If you wish to do this in geogebra, I will show you how easy it is.
7. What should the slope represent?
8. What do you find the fundamental frequency of the string to be?
Open Ended Pipe Resonance Modes
In this section you will find the resonance modes of the air inside a pipe that is open on one end. You can think of this as a model of an organ pipe. The pipe is open on the top and has an adjustable water column on the other end - to make the length of the pipe adjustable. Recall that a single, open end adds a reflective phase change that is not present in the closed resonance chamber.
You will be using a tuning fork as the source of the excitation for the resonance. When the tuning fork (acting as a fundamental) matches any resonance mode in the pipe (which may be multiples of the fundamental), it will cause the pipe to resonate and "sing" back. This is like pushing a kid on a swing at just the right times to induce a big swing. You can push the kid every swing, every second swing, every third swing, etc, and in all of those cases induce a large swing. What's different here is that the kid (pipe) has multiple swing frequencies (resonance modes) that you (the tuning fork) can excite. So the system is more complex than a kid on a swing.
1. Obtain a tuning fork and read the frequency off the fork and record it.
2. To save time, predict the approximate depth of column that will resonate at that frequency. Use the speed of sound in air as v=343 m/s.
3. Strike the tuning for ON A SURFACE THAT IS NOT HARD - like your knee or the edge of a book. The tuning forks are aluminum - a notoriously soft metal. If a fork gets dented it will have an effect on its ability to resound and potentially on its frequency of resonance.
4. Hold the fork with prongs downward just above the pipe and have someone else VERY SLOWLY vary the column depth around your starting value until the pipe "sings back" as loudly as possible. Just use your ear to discern this.
5. Record that depth as L1. Do this for the next two harmonics as well and record the depths.
6. Compare the theoretically expected depths to the measured ones and calculate the percentage error for each of them. Add to your measured depths 0.6D (where D is the inner diameter of the pipe). This is because it can be shown that the reflected sound waves near the open end of the pipe actually travel a bit beyond the physical end of the pipe, and 0.6D is a good approximation for that extra distance.
QUESTIONS
1. Which harmonics are present on the guitar string (by n value)?
2. Which harmonics are present on a pipe with one open end (by n value)?
3. Do pipes produce frequencies slightly higher or slightly lower than what you'd expect from just using their physical length as the length of the resonance chamber?