The Physics Philes, lesson 107: The Subjective Side of Physics
We’ve been riding waves for a while now, and last week we dove head-long into sound waves. Sound is particularly interesting, I think, because it’s really easy to illustrate how physics informs how our bodies react to external stimuli.
What you hear when you hear a sound is directly related to the sound wave’s physical characteristics. The greater the pressure amplitude (the maximum pressure fluctuation) of a sinusoidal sound wave, the louder it seems at a given frequency. Normally, in physics we can talk about laws that are universal, that are the same everywhere in the universe. In this case, though, the perceived loudness of a sound is in some ways subjective. It will vary from person to person. On reason for this is that the human ear is not equally sensitive to all frequencies in the audible range. A sound at one frequency can be perceived as louder as another sound that has the same pressure amplitude but different frequency. For example, at 1000 Hz, the minimum pressure amplitude to hear the sound with normal hearing is about 3 x 10^-5 Pa. To get the same loudness at 200 Hz, you need 3 x 10^-4 Pa.
Our physical response to sound – i.e. what we can perceive – changes with age. As we age, our ability to hear high-frequency sound waves will lesson. Also, it’s possible damage your hearing by listening to music too loud though ear buds or headphones, for example.
When you describe a sound as “high” or “low,” you’re describing the sound’s pitch. That also means that you are recognizing the sound wave’s frequency. The higher the frequency, the higher the pitch. But pitch is not totally the domain of the frequency. The pressure amplitude has a role to play, as well. If someone hears two sinusoidal sound waves that have the same frequency but different pressure amplitudes, the wave with the greater pressure amplitude will usually be heard as louder with a slightly lower pitch.
Musical sounds, as I have noted in previous posts, are complex. Wind instruments like the clarinet produce vibrations at a fundamental frequency and at many harmonics at the same time. The sound wave produced has a similar amount of each harmonic. In other words, the sound wave has a similar harmonic content.
Two instruments can be played at the same pitch (fundamental frequency), but they will sound different because of differing harmonic contents. The difference in sound is called the timbre. Again, we move into the realm of the subjective when describing timbre. We might say an instrument sounds “reedy” or “tinny.” This same principle applies to the human voice, as well. The vowels “a” and “e” sound different because of the difference in the harmonic content.
One more factor in determining tone quality is the behavior at the beginning (aka attack) and end (aka decay) of the tone. For example, a piano tone will start with a thump and slowly fade away. But a harpsichord tone will behave differently. It will begin more quickly and die out more quickly.
We’ve been talking about music so far, which is a lovely and beautiful use of sound. But we know that not all sound is beautiful. Sometimes it can be a cacophony. This is what we call noise, and it’s the combination of all frequencies, not just the frequencies that are integer multiples of a fundamental frequency. We all know about white noise, which is equal amounts of all frequencies in the audible range. But try making an “s” sound. That also fulfills the definition of noise.
That’s it for this week. Next week we’ll start looking at how quickly sound moves in various media.
Featured image credit: Timothy Swinson via Flickr