Build A Band of Musical Instruments
In order to build our musical instruments, we first have to start with the understanding that sound comes from vibration. When an object vibrates many times per second, the number of vibrations per second create compressions and rarefactions in the air that our ears pick up and process as sound waves. The more times per second an object vibrates, the higher the frequency, the shorter the wavelength, and the higher the pitch we hear.
There are many pitches and notes that that humans can hear within our normal hearing range of 20Hz (20 vibrations per second) to 20,000Hz. There are 8 or 9 octaves in the musical scale (depending on your range of hearing) and each octave has all of the notes (CDEFGAB). It is standard to base your instrument around "middle C" which is represented by the subscript 4 (C4, D4, E4, etc.). If you're looking for a higher pitched instrument, you could instead design around the fifth octave (C5), which has higher frequencies, smaller wavelengths and higher pitches. Because of the shorter wavelengths, higher pitched instruments tend to be smaller, such as the violin and the piccolo. If you're trying to design a lower pitched instrument with deeper notes, you might use the third octave (C3) which has lower frequencies, longer wavelengths, and thus lower notes. Due to the longer wavelengths, lower pitched instruments tend to be larger such as the bass or cello. I don't recommend building instruments using octaves lower than 3 or higher than 5 because your instrument would be either too large or too small for our classroom purposes. You can find the wavelengths and frequencies of all notes here.
When designing your string instrument, you can get different notes by changing the length of the string or the tension within the string. Most string instruments vibrate as one standing wave, which is half of one wavelength. As a result, a good starting point is to design your string to be half of the wavelength of the note you are trying to create. You can find the wavelengths of the notes at this site. You could create multiple strings for each note or you could add frets for the string to shorten it. Generally, thicker wires vibrate slower and have lower frequencies while lighter strings vibrate faster and create higher notes. It can be very difficult to tension thick wires. I've had good success using fishing line as the string for instruments. You can use thicker of thinner fishing line to see if it changes the pitch.
For wind instruments, the first thing you need to do is create a vibration. This can be done in a number of ways; the vibration can come from your lips as in a trumpet, it can come from a reed moving up and down as in a clarinet, or it can come from splitting the air like in a flute or a recorder. Once the vibration is started, it needs to propagate through a tube. Generally, a note will be made by a tube that is one quarter the length of the wavelength. This is because the air pressure is greatest at the mouth end of the tube and reduces to neutral atmospheric pressure at the open end of the tube. This change from crest to equilibrium in a wave is 1/4 of a wavelength and is explained in more detail here. That means that if you find the wavelength of the note you want to create, you need to send the compressed air down a tube that is one quarter that length. You can change the length of the tube by moving it back and forth like a trombone, or by making holes in the tube and then unplugging those holes. You can use the quarter wavelengths to determine the hole locations or a great resource to find the location of the holes is here.
Chimes are based on the natural frequency of a material. Every material has a different natural frequency and this can also be affected by the thickness or composition of the material. Some materials resonate better than others and produce a louder and clearer sound. Generally harder materials work much better than softer materials. EMT conduit is a pipe that is inexpensive and also resonates nicely. You can also make nice noise and notes from glass or hard woods. Generally, the length and size of the chime does not relate directly to the wavelength of the note. For help with chimes, I recommend looking at this site which can help find the ratio between chimes. Overall, a full octave has a ratio of square root of two between the notes. For example, C3 would be root two times larger (1.414x) of a chime than C4.
Here are a few more great resources to learn more about waves and sound:
Physics of Sound Comprehensive text
http://method-behind-the-music.com/mechanics/physics/ (also, check out the other pages on the sidebar of this page)
Sound Textbook Chapter