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A bugle and a whistle are essentially both tubes open at both ends. A bugle has no keys, yet you can play several notes on it. A whistle also has no keys, but it only plays a single note. Why is this?

What's the physics behind it?

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    This is genuinely one of the most interesting questions I've seen here in a while, and I'd love to see answers. Sans numbers and not in homework format, of course. – Some Dude On The Interwebs May 25 '15 at 23:16
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    Actually the premise is not correct. You can play the same harmonic series on a woodwind that you can on a brass instrument. The main difference I can think of is that on brass instruments, typically the root frequency is NOT easily played, and the sequence starts on the second tone of the harmonic series. IE, on a Bb Trumpet vs a Bb whistle. If you adjust your embrochure properly on the whistle you can play Bb, Bb octave, F, Bb, D, F, Ab, Bb, C, . . . The trumpet plays exactly this same sequence but starting on the second tone. On a pennywhistle you have to learn harmonics to play high. – Darren Ringer May 26 '15 at 0:58
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    Two other differences: the higher harmonics on a pennywhistle tend to be pretty out of tune, and the fundamental is high enough that you wouldn't have much use for them even if they weren't. – Micah May 26 '15 at 5:53
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    Worth mentioning: a decent player on a standard flute can play the fundamental and more than one overtone. While not as impressive as what a brass player can do, Darren Ringer does make a good point. Given a long enough tube (think bass flute here), a good player might be able to get 3 or more overtones from a tube with a woodwind embouchure. However, there's a limit to how large a tube could be used, because no one has lips big enough to blow an embouchure hole the size of a toilet bowl ;-) – Kevin_Kinsey May 26 '15 at 17:11
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    @DarrenRinger: A typical whistle behaves as a closed pipe rather than an open pipe; while an open pipe of a given length will have harmonics 1, 2, 3, 4, etc. the harmonic series of a closed pipe will be 0.5, 1.5, 2.5, 3.5, etc. [commonly expressed as odd multiples of a fundamental that's an octave lower]. – supercat May 26 '15 at 18:17
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On some types of whistle if you blow really hard you can get the second harmonic, sounding one octave higher than the fundamental. A recorder is essentially a whistle with the length of the resonating chamber controlled by the fingers, and you can very easily overblow an octave.

Brass instruments more easily play their overtones because you're in direct control of the vibration. Playing a brass instrument is essentially singing with your lips, with the instrument snapping the pitch to the nearest overtone. You don't have this kind of direct control over a whistle.

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    Usually if you play around a bit you can overblow/underblow the usual note, even on "ref" whistles. Whether the note will be pleasing audible is another question. – Josiah May 26 '15 at 18:55
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The reason that you can get multiple notes from a bugle is that you can vary your embouchure. If you tighten your mouth, and blow harder, you'll get a higher note because your lips move faster. The bugle is essentially an amplifier of the sound that you make with your lips. It can only amplify frequencies that it resonates to, which is why the bugle has a limited number of notes. (A trumpet has valves which in effect vary the size of the horn's airway, allowing it to resonate to different harmonic series.)

With a whistle, the embouchure is fixed. You blow in a hole. Another hole restricts the air flow coming out, causing the air to vibrate at a particular frequency which is a function of the volume of the inside of the whistle and the size and shape of the hole. If you blow harder you'll just affect the amplitude--you'll get a louder sound. (Contrast this with a slide whistle. By changing the size of the whistle, you get a different sized column of air, and so a different note. Also, a penny whistle gets different notes by stopping off different holes along the tube, which changes the size of the tube and hence the volume of air.)

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Summary

A whistle with a much smaller resonating chamber has only a very small set of frequencies it resonates at. A bugle, much longer with a horn on one end, resonates at many frequencies. Both start with broadband noise, but the whistle can only resonate at one frequency, while the bugle can resonate at several. Therefore the bugler can adjust the broadband noise to get the frequency they are interested in.

Noise source

Whistles and bugles produce sound in fundamentally different ways, however the result is the same - a relatively narrow but still broadband noise is introduced to the instrument's resonating cavity:

A whistle pushes fast moving air past slower air, producing vortices that create pressure waves. This results in broadband noise with a peak frequency. The chamber or tube which this noise is introduced to resonates at a specific frequency withing the broadband noise, and not only damps other adjacent frequencies, but reinforces the selected frequency. Notably, this broadband noise isn't very adjustable - you can blow faster or slower, but the design of the noise source limits the user's control over what the dominant noise frequency is.

A bugle player introduces broadband noise into the bugle by flowing air past the player's lips, which vibrate, modulating the air and creating the pressure waves. The user has a great deal of control in the dominant frequency introduced into the instrument. By adjusting the tightness of their lips, they can increase or decrease the frequency significantly.

Resonant cavity

When a wave is reflected back towards its source, if it's not in phase with the source, the reflection will damp or reduce the source. If it's in phase, it will reinforce the source.

In a whistle, the chamber or cavity is very simple, most often just a cylinder. It resonates at relatively few frequencies.

A bugle is a much more acoustically complicated instrument. Not only does the length of the tube create a long cavity which can resonate at many frequencies, but the bell at the end is a significant (and complex from a physics standpoint) part of the cavity. A theoretically "perfect" bugle would only resonate at the desired frequencies. Of course there are tradeoffs in the real world, and so the player still has significant work making sure they produce an initial noise that makes the desired note, but the bugle still damps most frequencies, and reinforces the desired frequencies.

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As a point of information, the three-hole tabor pipe, used in combination with a small drum as a 'pipe and tabor', uses the harmonic series of the pipe to produce 1 and a half octaves and theoretically more starting on the octave harmonic (the fundamental is rarely used). The Galician Txistu is basically the same instrument.

You can reproduce the same effect on a standard tin whistle by holding the top 3 holes closed and varying the breath pressure whilst playing the bottom three holes. The compromises in hole size and positioning made to keep the standard 2 octaves in tune mean that the overtones get more and more out of tune as you get higher.

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