Diddley Bow. (Sound Project) OBJECTIVES

Transcription

1 Diddley Bow (Sound Project) OBJECTIVES How are standing waves created on a vibrating string? How are harmonics related to physics and music? What factors determine the frequency and pitch of a standing wave? BACKGROUND Science: How do we make musical sounds? To make a sound, we need something that vibrates. If we want to make musical notes you usually need the vibration to have an almost constant frequency: that means stable pitch. We also want a frequency that can be easily controlled by the player. In nonelectronic instruments, the stable, controlled vibration is produced by a standing wave. If you pluck a string on a guitar or bass, you pull the string out at one point and then release it. The motion that follows is interesting, but complicated. The initial motion is shown below. However, the high frequency components of the motion (the sharp bends in the string) quickly disappear which is why the sound of a guitar note becomes more mellow a second or more after you pluck it. The string on a musical instrument is fixed at both ends, so any vibration of the string must have nodes at each end. Now that limits the possible vibrations. For instance the string with length L could have a standing wave with wavelength twice as long as the string (wavelength λ = 2L) as shown in the first sketch in the next series. This gives a node at either end, and an antinode in the middle. This is one of the modes of vibration of the string ("mode of vibration" just means style or way of vibrating). For a given wave speed, waves with different wavelengths have different frequencies. The mode with the lowest frequency (f1) is called the fundamental. All of the modes (and the sounds they produce) are called the harmonics of the string. The frequencies f, 2f, 3f, 4f etc are called the harmonic series.

2 What is a diddley bow? The diddley bow derives from instruments used in West Africa. It is typically homemade, consisting usually of a wooden board and a single wire string stretched between two screws, and played by plucking while varying the pitch with a metal or glass slide held in the other hand. A glass bottle is usually used as the bridge, which helps magnify the sound. The diddley bow is significant to blues music. Background Questions: 1) What type of wave is created when a violin is played? Explain. 2) What is the difference between a node and antinode? 3) What is a mode? 4) What is the fundamental? 5) What is a harmonic series? 6) Why are we building a diddley bow?

3 CAN WE BUILD IT? (YES WE CAN!) Directions: Use a pencil to mark the center line along the length of the broad side of the board. I then drive two 10 penny or larger nails into the center line about one inch in from each end, angling the nails so that they slope toward the ends of the board. Next, I take a length of 16 gauge galvanized steel wire and wrap one end of the wire around one of the nails for a couple of turns and then around itself. I wrap the wire around the other nail for a couple of turns (using pliers to keep it as tight as possible), and then around itself, and cut off the extra. I keep the wire close to the board at both ends, and try to get it as tight as I can. If the wire is too high on the nails, the nails will bend when the required tension is put on the wire. For the bridge, I use a small, cylindrical jar or bottle made of thick glass with straight, not tapered sides, such as a jelly jar, an instant yeast jar, or a hot sauce bottle. I slip the jar under the wire at the center of the instrument, and slide it toward one of the nails pushing it as far as it will go. Once the jar is in place, I then install what a guitarist would call the "nut." I slip a small scrap of wood (e.g., 1 x 2 or toy alphabet block) under the string and push it towards the other nail, pushing it as far as I can. I then use a small hammer to whack the wood nut (not the jar!) towards the nail. At this point, the wire should sound "bright" when struck with a stick. If it still gives a dull thump, the wire needs to be a little tighter. If the string is as tight as it will go with the current block of wood and still sounds dull, I would suggest trying a larger (taller) block of wood to increase string tension. A slightly more difficult solution is to use a larger bottle, or to restring, getting the wire a little tighter to start with. Remember, none of these things are terribly difficult. Video:

4 CAN WE TUNE IT? (YES WE CAN!) Online Tuner: Directions: Follow the link from above and open up the online tuner. The tuner will show you several different values and has a few different options. The main thing you will be looking at is the frequency of your note. Connect the microphone to your computer and place it near your diddley bow. Pluck your string and observe the frequency. You are looking for a somewhat constant frequency. Try plucking your string a few times to see if you can get a good reading. You want your diddley bow tuned to a C ( Hz) when the full string is plucked. Adjust your diddley bow s tension until your get a consistent reading. Once you have your diddley bow tuned to the first C. Pluck the string and slide your battery along the vibrating string. You should hear a change in pitch. Try placing the battery somewhere along the string so when it is plucked it produces a D note ( Hz). Mark this position on your diddley bow s board and record it in your data table. Continue using the same process from above, finding the rest of the notes and marking their position on the diddley bow and recording the results on your data table. Data Table Note Frequency (Hz) Position (cm) C D E F G A B C Length of string: cm

5 CONCLUSION: 1) Does increasing the tension in the string increase or decrease the pitch? 2) The length of the string that is free to vibrate is important. When you stop a string against the fingerboard you shorten the effective length. Does this raise or lower the pitch? 3) An ideal instrument produces a stable frequency that can be easily controlled by the player. Is your didley bow an ideal instrument? Explain why. 4) What advice would you give to someone who is attempting to build and tune a diddley bow? 5) How long would it take an A note wave to complete one cycle? 6) The speed of sound is 340 m/s through air. What is the wave length of a G note? (v = λf) 7) Using the position of the G note, calculate how many total wavelengths will fit on the vibrating string. 8) Draw a diagram of the G note. Label the wavelength, nodes, and antinodes.