What makes up our everyday symphony
Something I know I take for granted is the rich texture of sounds that I interact with on a daily basis. The clacking sound the keys make when I type out this blog post sound different to me than the music I listen to while I do it. As you probably already know, the wide array of sounds we experience each day are the result of sound waves doing their work.
Sound waves are fascinating, and are affected by many different physical phenomena. We can break down the components of a sound wave into intensity, propagation, pitch, and tone. I will analyze pitch, tone, and harmonics with more depth in a future blog. Let’s think of harmonics in a musical context: the note an instrument creates is primarily composed of the lowest frequency produced by an oscillation, the fundamental frequency. In addition to this, other sound waves that are just multiples of the fundamental frequency can be present, and these are called harmonics. The specific combination of the fundamental and harmonic frequencies are what allows us to distinguish the difference in sound between a clarinet and a piano, even if they are playing the same pitch.
For now, let’s focus on the propagation of sound waves, beginning with a look at intensity. The amplitude of a wave is a measure of energy, and is perceived by us as the volume of the sound. A smaller amplitude makes a quieter sound, and a larger amplitude will create a loud sound. The intensity of a sound is sound power per unit area, and can be measured in Decibels:
Where I is the given Intensity in watts/m2, and I0 is a standard threshold of hearing, 10-12 watts/m2.
As for the physical propagation of the wave, we are familiar with plane waves that move through three-dimensional space as a plane.
However, sound will frequently expand and travel through space in a spherical shape.
The intensity of the sound is distributed across the surface of the cylinder, and as the wave propagates and expands the intensity will decrease. The surface area of a sphere is proportional to the radius squared, so the intensity of a sound wave is inversely proportional to the radius squared. This weakening of the intensity in both square waves and plane waves explain why sounds further away are quieter than sounds generated right next to our ears.
Taylor wrote a great blog about sound wave propagation through different media. We can take this knowledge, and think about refraction, which involves the bending of a sound wave in one medium. A fun, naturally occurring example of refraction is temperature inversion, in which sound waves are refracted back to the ground as they travel higher in elevation at night or during particularly cloudy times. This occurs because air temperature decreases with elevation. It allows for sound to be heard more clearly over long distances at night rather than the day, which explains that nighttime quietness that we’ve all hopefully experienced at some point in our lives.
Reflection of sound waves is something we’ve definitely all experienced through echoes. We experience reflection of sound waves all the time, whenever a sound wave travels to another medium, or when the speed of the sound is changed in any way. Devices and structures can be constructed in different ways to focus different components of the sound wave. Many whispering chambers utilize the ellipse shape, and have structures at the focal point of the ellipses, which direct sounds to the other focal point of the ellipse.
Another important characteristic of wave propagation is acoustic impedance. It is the ratio of the pressure of the wave, p, over the volume flow of the air of acoustic flow, U:
The acoustic impedance tells us how much pressure a certain vibration of air at a specific frequency produces. The simplified formula above for acoustic impedance is only true if the wave is one-dimensional, and there are no reflections in the air column.
To understand this better, we can think of electrical impedance and consider the parallels. The changing electrical potential in physical space (V) brings about the moving charge (I) in the equation for electrical impedance:
In acoustic impedance, changes in the physical acoustic pressure brings about a change in air flow. The relationship between the pressure and air flow largely contributes to the way an instrument will sound and respond during each specific set of fingerings.
Also, because different media allow sound waves to pass through at different speeds, a sound wave traveling through will experience an impedance mismatch. The efficiency of the wave’s propagation can be enhanced by minimizing the mismatch between the source of the sound and the media it wants to pass into. For example, a piano’s string cannot produce sound efficiently enough by itself, so the sound wave it produces is sent to the soundboard, which is a large wooden plate that amplifies the sound, and transfers to the air—then the note is heard.
Hopefully this gives us a bit of a background to dive deeper into instrument harmonics soon, and a little more insight into how the sounds around us occur.