Guys I don’t want to come across as the thickie bass player here but how is it that a string can have different notes at the same length, i.e. if I tighten the string, the pitch goes up, even without the string shortening? I thought the wavelength was determined by the distance from bridge to nut.
Never noticed this before and it’s got me scratching my head…
Wavelength is proportional to the tension and thickness of the string, along with its length. And also the medium (i.e. material). For example, in air, the wavelength of the open E string is about 8 meters 
Not sure what the wavelength of 41Hz is in steel strings at rest but I would guess much, much longer than 8 meters. So, they need tension.
One thing that the string length does affect is how many of the higher harmonics of that wave will fit in the string, though, which is why longer scales sound brighter than shorter scales.
Aha - so the string is only vibrating at a fraction of its wavelength at any one time? That would make sense… Maybe if the length is set, and the pitch increases (when increasing tension) the speed of the wave increases as well?
I think I know this - these are multiples of the basic frequency of the string?
I’m not sure if that is it, or if the tension is used to reduce the wavelength in the string material down to the scale length. Or more accurately, since the wavelength is a function of all three, the tension changes the vibration frequency of a string at that length.
Yep!
Thanks! when you start thinking about it this is actually pretty complex stuff
I don’t know enough to answer all the questions, but on speed, an increase of frequency causes a decrease in length, but speed is constant. The tension of the medium has an effect on the speed, in fact the speed is entirely dependent on the medium. Not wavelenngth or frequency.
Yeah I think I can remember something about this from high school. Would the thickness of the string also affect the speed? I guess so. If all 4 open strings are at the same tension, they would have the same wavelengths.
And here I thought I understood stuff pretty well with “me pluck string, string make noise”.
Here, I rearranged it for frequency 
I was told there would be no math.
Yes (at least for the frequencies that humans hear) because if speed was dependent on wavelength or frequency, we’d hear low pitch at a different time than high pitch and that would really screw up the sound of an orchestra
Whoa that is like everything about strings ever! I even discovered a mandocello
I too have until now been happy to pluck a strong but not know how it works 
Wow that is pretty comprehensive!
On a related note, what I can’t wrap my head around is why the 4 saddles are not at the same position after the intonation is set correctly.
The 12th fret is supposed to be halfway between the nut and the saddle, because that’s how you get the octave (half wavelength, double frequency) at the 12th fret. If the distance from the nut to the 12th fret is the same on all 4 strings, then why is the distance from the 12th fret to the saddle not the same?
Angle, maybe? The strings are all at different heights at the saddle. That will change the length of the string.
I’ve thought about that and don’t know enough physics. The only variable is the thickness of the string. Right?
