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 agraff (piano—the constraint the speaking side strings pass through before the pins) on the other. The higher pressure wave inside a wind instrument tube reflects off the open end(s) because of a different 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
If you think harder, more reflective materials or media such as a wall create greater acoustic impedance and softer less reflective materials or media generate lesser acoustic impedance, the phase change of reflections is easy to predict. For longitudinal sound waves in air, if the softer incident force of the pressure wave reflects off a harder boundary, like a wall, there is no phase change 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, hits and reflects off the open end, which has lower acoustic impedance (being at atmospheric equilibrium), the reflection is flipped 180° out of phase to the incident. However, when it then reflects back off the opposite higher impedance closed end, it reflects back in phase. And a tube open on both ends, such as a flute, inverts the phase on both ends since the higher impedance of the air column is reflecting off the lower impedance of atmospheric equilibrium on each end.
Strings which are fixed on both ends and vibrate transversally, reflect 180° 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 off 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 agraff), and the waves spread out towards either fixed ends before they reflect 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, which is what contributes 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.
The string is plucked towards one end, which sets up stronger upper partials, represented by the smaller ripples.Simulation created with free Falstad applets at www.falstad.com. Try them!