0.2 Another way of viewing the world

Up to this point, we have mainly focussed on waves as a function of time. Now what do we mean by a function of time? Well, in Understanding Wave Jargon; Building Waves on Strings Intuition , wiggling the end of the string affected how the rest of the string responded in time. In other words, we are used to seeing everything as causal because our actions have consequences that we observe. If I eat too much, I get a stomache ache an hour later. If my ears are ringing, it wouldn't be surprising if I had just come out of a rock conert.

Well, another way of seeing events is in the frequency domain. Now what does this mean? As described in Talking about Sound and Music and Frequency, Wavelength, and Pitch , frequency is the number of times a wave occurs per second. However, the concept of frequency does not have to apply to just waves. It can apply to any event, observation, or even concept that occurs multiple times. For example, one can say that the sun rises at a frequency of once per day. One can also say that in each year, a season changes once every three months.

Now why should you care? What possible relevance does this have to your daily life? Well, as discussed in Talking about Sound and Music , pitches that our ear hears correspond to waves; and since waves have a regularity of repeating itself, all pitches that we hear have frequencies associated with them. Note that the pitches we hear do not necessarily correspond to one frequency. For example, when you strike a string on a guitar, you hear not waves of a single frequency, but the sum of many waves with differing frequencies. However, when striking the strings of an instrument or blowing into a wind instrument, the frequencies that the resulting sound/wave has, is not accidental or random. There is a theory/pattern behind it, but we will not delve into that at this point.

Since the pitches we hear in music typically have flavor to them, in musical terms, differing timbre, (ie. the different sound we hear when playing the same pitch on a guitar and clarinet), most of this phenomenon corresponds to differing spectrograms (graphs of the frequency domain). To solidify this concept, we will provide a few sound examples and their corresponding spectrograms. Don't worry, there'll be plenty of explanation.

Below, I have provided two recordings. One is a recording of me striking the 'A' string of my guitar. The other is a recording of striking the high 'E' string of my guitar.

Plucking the 'a' string of a guitar

There are a few things to note. In Figure 2, we notice that the sound peaks as it is struck and decays to zero close to 8 seconds. This should resonate well with your intuition from hearing the sound file. Now in Figure 3, you'll notice that there are patterns to the signal heard. Furthermore, you'll also notice that there is not just one wave of a single frequency, but that you can eyeball several waves. For example, there is the large wave that has higher signal than other parts of the wave, as there also appears to be a cross of two waves with higher frequencies in the signal.