Chapter One: An Acoustics Primer

11. What is reflection? | Page 2

Other Types of Reflection

On the previous page, we discussed reflection of propagating sound waves in air. However, other important types of reflection to consider include reflection of constrained stretched strings, such as in violins, guitars or pianos, and reflection of narrow air columns, for example in wind instruments. String instruments normally constrain the string on both ends via a bridge on one end, and a nut or agraffe—the metal termination piece that constrains the speaking length of a piano string before the tuning pins—on the other. The higher pressure wave inside a wind instrument tube reflects off the open ends due to a difference in atmospheric pressure. In all these instrumental cases, in order to function musically, these reflections set up standing waves at resonant frequencies.

Phase Change of Reflections

Considering that harder, more reflective materials create greater acoustic impedance, whereas softer, less reflective materials generate lesser acoustic impedance, the phase change of reflections is highly predictable. For longitudinal sound waves in air, if the softer incident force of the pressure wave reflects from a harder boundary, such as a wall, no phase change occurs upon reflection. This is what contributes to the doubling of constructive interference amplitude at the pressure zone. If a higher impedance incident force, such as an air column pressure wave in a tube open on only one end, strikes and reflects from the open end, which has lower acoustic impedance—which rests at atmospheric equilibrium—the reflection is flipped 180 degrees out of phase to the incident. However, when it then reflects from the opposite higher impedance closed end, it reflects in phase. And a tube open at both ends, such as a flute, inverts the phase at each boundary because the higher impedance of the air column encounters the lower impedance of atmospheric equilibrium on each end.

Strings fixed at both ends that vibrate transversally reflect 180 degrees out of phase on both ends, while a string with a "free" end will reflect in phase on that end (I can't think of any instruments that are so configured, unless you compose for whips). So strings act inversely to air columns when reflecting from a boundary. Interestingly, many strings, such as those of a guitar or piano, are bowed, plucked or struck somewhere other than either end (guitar, nearer the bridge, piano mostly nearer the agraffe), and the waves spread out towards either fixed end prior to reflecting in reversed phase. When they meet again after reflection, there is likely constructive and destructive interference occurring before the note "settles down" to mode-locked standing waves if they are bowed. This is a fancy way of saying the competing interferences create a feedback system in which they come to an agreement and produce perfect harmonic partials (1ƒ, 2ƒ, 3ƒ...). The mode-locked result is not as perfect if strings are plucked or struck; this phenomenon contributes directly to the inharmonicity of piano strings, for example. Guitarists and string players are able to take advantage of this by playing closer or farther from the string's end (marked sul ponticello or sul tasto respectively by composers) to manipulate the strength of partials—pianists are out of luck unless they are plucking or muting inside the piano.