Waves nodes and antinodes in a musical instrument

trumpetb

Member
Ive done a bit of research on this.

The cause of my research is unhappiness at the results experienced by players of valve leakage while logic suggests that this should not happen if a musical instrument is simply an open tube and behaves like one.

Clearly something else is at work here because the players must be correct due to the weight of evidence and logic must be wrong probably due to the lack of credible information that could explain the players experiences.

The research I have conducted has revealed the following statement link here Physics Tutorial: Nodes and Anti-nodes

A standing wave pattern is an interference phenomenon. It is formed as the result of the perfectly timed interference of two waves passing through the same medium. A standing wave pattern is not actually a wave; rather it is the pattern resulting from the presence of two waves of the same frequency with different directions of travel within the same medium.

What this means is if two waves of the same frequency exist but travel in opposite directions in a tube then a standing wave is created as an interference pattern.

So how does this complex state of two opposing waves come about, The moment a note is sounded a complex chain of events happens. One wave - the note, travels from mouthpiece to bell and then the instant the wave hits the bell rim a reflected wave of the same frequency immediately travels from bell to mouthpiece and it is this opposing wave that creates the standing wave in the instrument.

Blowing air into the instrument will not in itself cause air leakage past the valves however the two opposing waves cause the standing wave by differential pressures between nodes and antinodes within the instrument.

Both waves must be of the same frequency because the second wave is simply a reflection of the first so a standing wave is forced to exist within the tube.

The result is increased pressure throughout the instrument and at the valves which then attempts to escape the instrument and it then forces its way past the valves.

The effect of resistance to blow that many players experience is also now easily explained by this phenomenon. Increasing the pressure by blowing harder causes an equal and opposite increase of pressure that travels back through the instrument because the second wave is a reflection of the first and carries the same characteristics of the first wave including the pressure.

In effect the harder you blow the more the reflected wave will oppose the blow and you will feel resistance, and it is not the tubing or the size of that tube or its constrictions or wrap that is the culprit but the existence of the reflected wave that causes the opposing force to the first wave and this is felt as resistance.

It is not then the size of the tube or the number of bends in the tube that cause resistance although both these may have some effect and add to the resistance to some degree, but it is the complex and varying pressures between nodes and antinodes in the standing wave itself that are the root cause of the resistance and of the leakage.
 

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