Music and Mathematics – Part Two: The Nature of Sound

Ok, let's look at the second installment of my series on Music and Mathematics, namely, the Nature of Sound.

What is sound? Sound is a result of small vibrations in the air around us. Each point in the air has one pressure value, and this influences the pressure of the air around it. Sound waves can be easily visualized using a device called an oscilloscope, which plots sound as a function of time. What results is an image like this:

As you can see, it is quite difficult, if not impossible, to tell the nature of the sound simply from the oscilloscope tracing. Sounds actually differ only when you look at the bigger picture, and trace the sound over a period not of a hundredth of a second, but of three or four seconds. The sound will change slightly in amplitude and in frequency over the course of the tracing, and the way that it does this can lead to clues about what instrument produced the sound.

Sound waves, and the ways through which they are produced, have a few properties. First, the frequency of the sound, measured in Hertz (Hz), or number of vibrations per second, is 1 ÷ the time it takes for one full vibration to be completed. The higher the frequency is, the higher the pitch of the sound. When a string instrument, for example, is used to create the sound, the pitch is influenced by the string thickness, density, and length. As the tension increases, the pitch increases; however, as the thickness, density, or length increase, the frequency and the pitch of the sound decrease. 
 

Photo Credit: Oscilloscope via paleotechnologist.net, cc