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If you were to play a flute, you would want to blow sideways across it, kind of like a bottle, like in Fig 1. Why would this be better than blowing straight in to the hole, like in Fig 2? It seems like more air would go into the flute, which seems like a good thing, so why is it that you blow sideways?

Blowing into a flute sideways, the correct way.

Blowigng straight into a flute, the incorrect way.

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    $\begingroup$ Why would it be a good thing if more air went into the flute? It's already full of air. ;) $\endgroup$
    – PM 2Ring
    May 7 '20 at 5:18
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    $\begingroup$ Might I suggest that it's not a case of "have to", since there are a number of wind instruments that work by blowing "straight into the hole". Seem as though it's more about the ease of holding the flute - though I am not a player of any wind instrument. Maybe some flute players could comment? $\endgroup$
    – jamesqf
    May 7 '20 at 16:16
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    $\begingroup$ @jamesqf, it is nothing to do with the ease of holding the flute. The only way to get a musical note out of a flute is to blow sideways into it. $\endgroup$
    – TonyK
    May 7 '20 at 20:30
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    $\begingroup$ @TonyK: But that is due to the way it's constructed. There are plenty of flute-like instruments that are blown from the end: en.wikipedia.org/wiki/Flute $\endgroup$
    – jamesqf
    May 8 '20 at 2:36
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    $\begingroup$ +1 for the drawing $\endgroup$ May 10 '20 at 19:16
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How to create a sound?

To create sound, you would first need to create some kind of a wave, some kind of an oscillation. In the case of a flute, an oscillating column of air works very well, because the flute (its body) resonates at particular frequencies of oscillation and thus you can hear a sound.

What happens when you blow sideways?

Now to create a wave, we need to setup an oscillating jet of air. This is what exactly happens when we blow sideways into the flute. Why? Here's how:

flute

Image source

As you can see in the above image, when we blow a jet of air sideways, the blown air "collides" with the surface of the flute on the other side. You might expect that the air jet would get divided into two parts after striking the surface of the hole, but that's not what really happens$^{\phi}$. Instead, the jet of air rapidly fluctuates between going all into the hole and going all away from the hole. This sets up a rapid vibration at the end of the flute. Once this oscillating air column is set up, the flute's body does the job of amplifying the sound by resonating with this oscillating air column at particular frequencies.

Also, you might have to change your blowing pressure for playing different notes (which is expected) because the blowing pressure corresponds to the speed of air jet, which in turn corresponds to the frequency of the oscillation of air jet (See $[1]$ for further information). Also see this question on PSE which delves deeper into the relation between air jet speed and frequency.

What if I blow straight into the hole?

If you blow straight into the hole, you will not be able to setup any kind of air oscillations, except the fluctuations of your blown air. In this scenario, the blown air would simply enter from one end of the flute and exit from the other, producing nothing but some noise (due to the fluctuations of the air you blowed).

$^{\phi}$ Why does the air just not simply get divided into two parts instead of oscillating?

As the breath is directed toward the edge of the hole, high-pressure sound waves pass through the tube and reach openings such as the end of the foot joint and the sound holes. These waves then bounce back and try to force the air in the vicinity of the embouchure hole back out through the embouchure hole. As this happens, the sound pressure in this section of the instrument falls, and air is sucked back in. Waves are then produced that cause the air around the edge of the hole to vibrate up and down, producing changes in the sound.$^{[3]}$

Further reading/References

$[1] :$ https://newt.phys.unsw.edu.au/jw/fluteacoustics.html

$[2] :$ http://www.markshep.com/flute/Acoustics.html

$[3] :$ Yamaha's guide on how flutes work and more

$[4] :$ Working of a whistle

$[5] :$ Working of brass instruments

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    $\begingroup$ @AlexanderJ93 Well the link $[1]$ has nicely written it like this: "To play a high note, the travel time of waves on the jet must be reduced to match the higher frequency, and this is done by increasing the blowing pressure (which increases the jet speed) and moving the lips forward to shorten the distance along the jet to the edge of the embouchure hole. These are the adjustments that you gradually learn to make automatically when playing the flute. Flutists are usually taught to reduce the lip aperture when playing high notes." $\endgroup$
    – user258881
    May 7 '20 at 13:55
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    $\begingroup$ It's worth pointing out that reed instruments achieve the same effect by the vibration of the reed. $\endgroup$
    – Kai
    May 7 '20 at 15:49
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    $\begingroup$ @Kai: And that brassists need to buzz their lips to get the same effect. $\endgroup$
    – Vikki
    May 8 '20 at 0:49
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    $\begingroup$ @knzhou Thanks :) And about the working of brass instruments and whistles, I suppose it's better not to extend this answer, since I want the answer to be concise and mainly focused on the question. But you are also right that I should provide some kind of information about those instruments, and that's why I have added two relevant links regarding those instruments' working. This will help in keeping the answer to the point and will also allow curious readers to further explore about those instruments using the links. $\endgroup$
    – user258881
    May 8 '20 at 7:30
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    $\begingroup$ @Paul92 The reference $[3]$ says: "As the breath is directed toward the edge of the embouchure hole, high-pressure sound waves pass through the tube and reach openings such as the end of the foot joint and the sound holes. These waves then bounce back and try to force the air in the vicinity of the embouchure hole back out through the embouchure hole. As this happens, the sound pressure in this section of the instrument falls, and air is sucked back in. Waves are then produced that cause the air around the edge of the embouchure hole to vibrate up and down, producing changes in the sound." $\endgroup$
    – user258881
    May 8 '20 at 14:00
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that's because the objective is not to blow air into the flute, it's to excite a resonant mode in the air contained within the flute tube. When you blow across the flute opening, you are producing a burst of white noise at the flute opening, and the flute then filters out the frequencies (and overtones) at which it is resonant with that particular set of finger positions on the holes and that particular tone then quickly gains volume.

Once the flute starts resonating, then the back-and-forth motion of the air at the opening will begin to "steer" the airstream from your mouth into and out of the hole, strengthening the resonant tone.

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    $\begingroup$ Thank you, this was very informative, the filtering of white noise was new information for me. But I'm still somewhat confused as to why blowing directly into the flute wouldn't produce the same effect. $\endgroup$
    – Derian
    May 7 '20 at 6:32
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    $\begingroup$ Try this: you can blow a note on a beer bottle, yes? try blowing straight down into it versus sideways, across the open end. $\endgroup$ May 7 '20 at 6:36
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    $\begingroup$ Nice explanation. This is definitely the most intuitive, to me. $\endgroup$
    – Noldorin
    May 7 '20 at 22:17
  • $\begingroup$ Good answer, but it's probably worth also addressing why you do make sound in other instruments by blowing directly into them, such as most other wind instruments, and whistles. $\endgroup$
    – knzhou
    May 8 '20 at 5:36
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    $\begingroup$ @knzhou you don't really blow into a whistle / fipple flute either, though it looks like it. The labium still directs much (most?) of the air away from the main resonance tube. $\endgroup$ May 8 '20 at 11:18
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The principal difference between a flute and a flageolet is that in one the oscillation is triggered by blowing sideways, in the other you blow along the instrument. This does create differences in tone (harmonic content). Also, for the flageolet, a much more precise direction of flow is needed to create the sound, meaning that the instrumentalist has less scope for subtle control.

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    $\begingroup$ This is "correct" so far as it goes, but irrelevant to the OP's question. In the flageolet and recorder, the air stream that you blow "into" the instrument is directed across a hole to produce the tone in exactly the same was as in a flute. See en.wikipedia.org/wiki/Recorder_(musical_instrument)#/media/… for example $\endgroup$
    – alephzero
    May 8 '20 at 1:56
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You blow the flute by exciting its resonant frequency, which are special wave solutions along the longitudinal direction fo the flute, with waves of air density propagating from one end to another.

A resonant or stationary solution exists as a superposition of waves propagating forwards and backwards. So at least a large proportion of the driving force(your blowing the air) has to reach the other end. And somehow blowing directly into it wouldn't create a strong enough longitudinal wave that reaches to the far end. Also, maybe the wave that reflect from the far end will interfere with the air you blow straightly into the hole.

Above is only my speculation and I'm not sure which phenomenon contributes the most to the case. Any criticisms and clarifications would be very welcome.

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