guitar strings and speed

[gazza]

Hi all,hope someone clever can help me think my questions through.

I'm wondering a number of things. Firstly, what is the maximum speed a guitar string moves when plucked?

To expand further, a C string for example has a fundamental wave. When pulled back and released ,the string must accelerate to a maximum speed then slow down to a stop, then travel in the reverse direction ,oscillating back and forth until it comes to rest.

To complicate matters,to my understanding the string will vibrate with harmonics of which these will be integers of the standing wave. The string appears to have nodes or points at which the string is not moving but at other points it is moving between two maximum points in space at X speed.

Will the string be moving at greater speed for the harmonic portion of the string( giving those higher frequency harmonics) that the standing wave portion?

I feel I may be missing some fundamentals involving frequency/ wavelength & mass and velocity relationships.Thanks in advance for helping my poor brain out:D

[John Cuthber]

It depends how far it is streched away from straight. A bigger displacement will give a bigger velocity.

[swansont]

It depends how far it is streched away from straight. A bigger displacement will give a bigger velocity.

 

No, actually; this is a common misconception. The speed depends on the tension and the mass per unit length.

 

http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/string.html

[tomgwyther]

I suppose, the maximum speed a guitar string can move as pretty much infinite, as long as you have a very sturdy guitar and the string doesn't try to go faster than C (Speed of light) Music at near light speed pretty much died out in the early 90's.

 

It's true that the harder you twang a string, the faster it will move, otherwise the frequency or 'note' would change depending on how aggressively you played.

 

Think of it a bit like a pendulum on a clock, which oscillates once per second (1Hz) If you pull back the pendulum further it will still oscillate at the same frequency, but move faster.

 

Harmonics do complicate matters a bit. It's safe to say that a guitar string can oscillate with no harmonics, although the player can force a harmonic or harmonics to occure.

A guitar (If you have one) is a great way to illustrate what happens with harmonics because you can see it happening.

1. pluck the string exactly in the middle and you get a pure sine wave with no harmonics

2. pluck the string at either end and the wave form although uniform takes on a more jagged appearance

3. place you finger exactly halfway along the string as a damper (12th fret) and then with the other hand, pluck it.

What you'll see is that the area in the middle of the string doesn't vibrate but the area either side of this point vibrate twice as fast

4. If you place your finger 1/4 along the string and pluck it, you'll have three points where the string doesn't vibrate and four areas where it oscillates four times as fast.

 

if you get it just right, you can have both the sine wave and the harmonics coming from one string.

 

Some instruments rely on harmonics in this way, for example the notes on a xylophone or glockenspiel and on some wind-chimes are fixed in place at the 1/4 interval and thus are always playing harmonics of their standing frequency.

if you can (As I just have) take the chime from a glockenspiel, throw it in the air and hit it whilst it's in flight,then put it back in the instrument's frame and hit it again, you get two different tones.

 

Hope this is of some help, I shall now put my oscilloscope, my guitar, and my slightly damaged glockenspiel away!

But what the good of running a music studio if you can't play science-boy occasionally.

[Cap'n Refsmmat]

A guitar (If you have one) is a great way to illustrate what happens with harmonics because you can see it happening.

1. pluck the string exactly in the middle and you get a pure sine wave with no harmonics

I just tried this. There are still plenty of harmonics; the amplitudes of the harmonics are just different compared to when you pluck it elsewhere.

[swansont]

If plucking the string results in an initial distortion that is not a sine wave, you will get harmonics, since they are initially present — all the Fourier components of the initial shape of the string.

[npts2020]

If a guitar string exceeded the speed of sound, wouldn't it make a sound like a whip rather than a musical note (at least till is slowed below the speed of sound).

[tomgwyther]

Good point, I guess a guitar string couldn't exceed the speed of sound, at least not very easily.

It would be fun to find out what would happen if it did.

[John Cuthber]

No, actually; this is a common misconception. The speed depends on the tension and the mass per unit length.

 

http://hyperphysics.phy-astr.gsu.edu/Hbase/waves/string.html

 

That's interesting because it means that it still moves at that "magic" velocity when the sound has dies away and it's actually stationary. (I'm ignoring the quantum effects for simplicity).

 

Somehow I doubt that.

 

The speed that a wave runs up and down the string depends on the properties you mention, but the speed of the string is dependent on the amplitude of vibration.

When you pluck the string you stretch it and that stores potential energy in the string. When you let it go that potential energy is converted to kinetic energy. Since relatively little energy is lost as sound (during any one vibration of the string) the square of the string's peak velocity is roughly proportional to the initial displacement.

Of course, there are potential problems as the speed of the string reaches the speed of sound- not least the assumption that the rate of energy loss is small is no longer true.

[swansont]

That's interesting because it means that it still moves at that "magic" velocity when the sound has dies away and it's actually stationary. (I'm ignoring the quantum effects for simplicity).

 

Somehow I doubt that.

 

The speed that a wave runs up and down the string depends on the properties you mention, but the speed of the string is dependent on the amplitude of vibration.

When you pluck the string you stretch it and that stores potential energy in the string. When you let it go that potential energy is converted to kinetic energy. Since relatively little energy is lost as sound (during any one vibration of the string) the square of the string's peak velocity is roughly proportional to the initial displacement.

Of course, there are potential problems as the speed of the string reaches the speed of sound- not least the assumption that the rate of energy loss is small is no longer true.

 

 

Ah, yes. We're talking about different phenomenon. I misinterpreted the OP. My bad.

[gazza]

thanks for your interesting and informative replies folks.I now understand about String theory ;-)

However ,this got me thinking about light and the electromagnetic spectrum. Is there a theoretical limit to how high the frequency that the gamma ray spectrum can go?

I thought that the more energy put into a photon would just increase the amplitude of the waveform,i.e, it's intensity rather than it's frequency.

So what "adjusts" the frequency of light/elctromagnetic waveforms?

Taking the guitar string analogy, of the string being fixed between two points in space,could the same be said of a wave of electomagnetic form?

I know that visible light wavelengths are measured in nm,and that the scale becomes so small at gamma ray wavelengths that it has to be measured in electron volts instead,I just wondered if the theoretical "string" length of gamma rays is limited to quantum foam scale,therefore there is a frequency limit.

Look forward to reading your replies.

Thanks.