Quake3World

Preparing for a lesson tomorrow - i'm tutoring a grade 11 physics student and high school physics has changed a lot in the 10 years i've been out of it.

I've taught myself a bit about fundamental frequencies, standing waves, resonant frequencies, and harmonics, and their relationships to each other from this page:

http://www.glenbrook.k12.il.us/gbssci/p ... 11l4a.html

but i have a question:

say you have a guitar string at a certain tension and certain length, and you pluck it.

Will you only elicit the fundamental frequency? Or will you elicit the fundamental frequency + a few harmonics simultaneously?

Would there be a way to elicit individual harmonics in isolation if you plucked it a certain way? What would that way be?

I know with a trumpet you can do it by altering the air pressure (I presume that's why you can get many pitches even though you only have three buttons).

(I know that you wouldn't need to isolate harmonic frequencies to play the guitar, since you can just alter the length - but my question is specifically a hypothetical one about a fixed string length and tension).

You will always elicit the fundamental and harmonics, but the contribution of each to the overall signal depends on various properties (string material, how it's made, how it's attached, what it's attached to, etc). As far as the equations go...you're on your own for that.

Canis wrote:You will always elicit the fundamental and harmonics, but the contribution of each to the overall signal depends on various properties (string material, how it's made, how it's attached, what it's attached to, etc). As far as the equations go...you're on your own for that.

AND how you're "plucking" or "picking" the string, the resonance and acoustics of the room, what you're wearing, etc.

i have a huge exam on physics in a week, a large part of it being on sound (harmonics and resonant frequencies and stuff).

i tried to answer the guitar harmonics question but realised i got it horribly, horribly wrong. if you have questions, i'll get my crazy smart friend doing physics also to answer anything you can throw at him

glad that crap is over

such a waste

Fundamental + harmonics. To fully describe the phenomenon mathematically, you'll need Fourier series or Schroedinger's wave equation. I doubt that your 11th graders are up to solving partial differential equations, so I wouldn't worry about it.

schroedinger....that bastard.

i heard he killed his cat



or did he?

No but he did win wimbledon once.

hate wrote:glad that crap is over

such a waste

lol so true

YEAH, LEARNING SUCKS! IGNORANCE AND MEDIOCRITY FUCKING ROCK!

its nice to have fantasy fun

thanks Canis, jug, nightshade

so to clarify, the vibrating air chamber inside a trumpet is somewhat different from a vibrating guitar string in that you can isolate harmonics in a trumpet but not a guitar right?

I don't think that it's a question of isolating them as it is amplifying them.

Nightshade wrote:I don't think that it's a question of isolating them as it is amplifying them.

ah i c.

and you can do this in a trumpet because your lips have a much finer control over air pressure than your fingers do while strumming a string i'm guessin.

Then there's the valving as well. IIRC, the fundamental and harmonics are always present, but it's the way the system is tuned that determines which has the largest amplitude. I wish I had my physics book with me, but I'm at work.

ok one more question:

a guitar string has fixed ends, and thus a standing wave is what produces the sound.

but a trumpet has an open air chamber right? So if the sound wave isn't reflected, how can you have harmonics?

(or is it reflected?)

[xeno]Julios wrote:thanks Canis, jug, nightshade

so to clarify, the vibrating air chamber inside a trumpet is somewhat different from a vibrating guitar string in that you can isolate harmonics in a trumpet but not a guitar right?

You can isolate harmonics on the guitar string at different node points along the string. For eg the 12th fret harmonic is the same as the normal 12th fret note.

Applying a light touch to the string at different node points isolates the different harmonics at the 3rd, 5th, 7th and 9th frets. It's been fucking years since I played guitar...so I might be a bit off with my "knowledge" on this.

I was eyeballing a nice Carver axe the other week...I just might pick it up again.

[xeno]Julios wrote: a guitar string has fixed ends, and thus a standing wave is what produces the sound.

but a trumpet has an open air chamber right? So if the sound wave isn't reflected, how can you have harmonics?

The same way a trumpet does it...amplification.

MKJ wrote:i heard he killed his cat



or did he?

I say yes...and no.

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GONNAFISTYA wrote:

[xeno]Julios wrote: a guitar string has fixed ends, and thus a standing wave is what produces the sound.

but a trumpet has an open air chamber right? So if the sound wave isn't reflected, how can you have harmonics?

The same way a trumpet does it...amplification.

what?

+JuggerNaut+ wrote:

GONNAFISTYA wrote:

[xeno]Julios wrote: a guitar string has fixed ends, and thus a standing wave is what produces the sound.

but a trumpet has an open air chamber right? So if the sound wave isn't reflected, how can you have harmonics?

The same way a trumpet does it...amplification.

what?

Maybe I misunderstood the question. I was standing up at the time.

The harmonics come from the length of the tube, just like the length of the string. Your lips pressed against one end are providing a "mouth" for the trumpet tube's length to act upon. The frequency of the changes in pressure determined by the tube length act upon one's pursed lips, modulating the frequency coming out of those lips. It's just like a pipe organ or flute. One provides a steady stream of air to the "mouth" of the pipe, from your lungs to your lips for a trumpet; from your mouth accross the hole of a flute; or from your lungs to a reed of a sax) and then the fluctuations of pressure according ot the length of the tube feed back on the point of vibration (the mouth) and modulate that vibration according to the length of the tube.

The harmonics associated with each pitch are present as 2x, 3x, 4x, 5x, etc. of the base frequency, and add to the brightness and tone of the instrument.

Now in the case of a bugle, which doesnt have length modulation, one must change the vibration frequency of one's lips in accordance to the fundamental frequency and harmonics of the bugle itself. So there's the base note, then there's the octave above it (1st harmonic), then there's the 5th above that (2nd harmonic), and then the 3rd above that (4th harmonic), then the 2nd above that (5th harmonic), etc.

The open-ended or closed-ended pipes just lengthen the pipe. For a pipe organ or a flute that have a mouth built into the pipe, closing the top of hte tube will lower the pitch one octave. For a trumpet, the mouth is at the end of the tube and not on the side, so air pressure isnt escaping from the side; rather, it's escaping from the open end so you'll just block the pressure changes and kill the sound. This is similar to if you were to cup your hand around the mouth of a pipe organ tube.

Canis wrote:The harmonics come from the length of the tube, just like the length of the string. Your lips pressed against one end are providing a "mouth" for the trumpet tube's length to act upon. The frequency of the changes in pressure determined by the tube length act upon one's pursed lips, modulating the frequency coming out of those lips. It's just like a pipe organ or flute. One provides a steady stream of air to the "mouth" of the pipe, from your lungs to your lips for a trumpet; from your mouth accross the hole of a flute; or from your lungs to a reed of a sax) and then the fluctuations of pressure according ot the length of the tube feed back on the point of vibration (the mouth) and modulate that vibration according to the length of the tube.

hm - still a bit confused - when i pluck the string, the energy is transmitted to the string, and a wave is formed along the string. Since the string is fixed at the ends, the reflected wave and incident wave produces a standing wave pattern. The harmonics are just those standing wave patterns which are coherent with regular nodes/antinodes.

But with a wind instrument, I'm unclear about what the "fixed" ends are. I'm taking it one end is your lips?