Frequency on woodwind instruments
Alto flute
Modify pitch by constant velocity
If we want to play different pitches on a musical instrument, we need to modify the sound frequency. But from physics, we have learnt that sound has a constant velocity at a given ambient temperature, which is
v = 340 m/s
So how do we control the frequency of a sound when playing instruments? You can't make a sound go any faster through the air, so you have to control the wavelength.
Let's look at a simple wooden flute as our model, and simplify its vibrations to be just the fundamental frequency.
Suli (transverse flute)
Changing pitch by modifying wavelength
When a person blows into a flute, it creates a sound wave inside of the flute.
Because the flute is closed on one end, that means that the sound wave must be zero at that end, because there isn't any leeway for the air molecules to move.
On the other end, where it's open, it's actually also restricted. Going from closed air to open air is a sudden change in pressure that causes the wave to have a bit of a bounceback effect that inverts it.
It can therefore only alternate between the lowest part of the wave and the highest part of the wave.
This means that all of the waves created that don't fit these requirements are cancelled out by the shape of the flute, leaving you with the one that does fit: a one-quarter wave that fits the length.
It is also what is called a standing wave, which is how it is oscillating but not moving across space. The waves it triggers at the end of the flute move outwards normally at the same frequency as the standing wave.
Modes of vibration of fixed string
Shows the modes of vibration of string fixed at both ends. You can choose the modes by altering the harmonic slider.
The trace enables you to see the appearance of the string over a period of time.
You can show or hide the markers for the nodes and antinodes.
You can also show the waves that are incident and reflected at the right hand boundary. (Roles are reversed at the left hand boundary.)
Changing pitch by modifying wavelength
If one quarter of the wave is the length of the flute, that means that the whole wave must be four flute-lengths.
So if a short flute will make a wave with a small wavelength, that means that it must also have a high frequency. If you can control the wavelength, that means controlling the pitch.
This is why covering and uncovering holes on a flute changes its pitch - it functionally changes the length of the flute because the closest hole that the air escapes from becomes the new "end" of the flute.
Harmonic vibration
References
Bryan H. Suits. (2021). Tuning. Physics of music notes. Michigan Tech University.
Question 1
How many antinodes are there in the nth harmonic
Question 2
How many nodes are there in the nth harmonic
Question 3
The nth harmonic is observed on a string of length L. What is the wavelength of the vibrations of the string?