5th harmonic or something else

Glen Herrmannsfeldt wrote:
> Richard Dobson wrote:
> (snip)
> 
>> It is also a practical matter - the core of a wound string is 
>> relatively narrow-gauge, making it as easy to wrap around tuning pegs 
>> and pins as the higher-pitch ones.  And for instruments where the hand 
>> is in direct contact with the string, clearly thickness has to be kept 
>> to a  minimum while obtaining the necessary pitch range.
> 
> I only recently got to try an electric guitar.  I was
> somewhat surprised on the thickness of the low strings.
> (I didn't have a pick so was doing it by hand.)


The frequency of a limp string's fundamental is equal to v/(2*L). where 
v is the velocity of a transverse wave on the string. and L is the 
distance between the bridges. (The factor 2 arises because L is a half 
wavelength.) In turn, v = sqrt(T/(m/l), where T is the tension and m/l 
is mass per unit length, rho. Since m goes as dia^2 and T/dia^2 is 
proportional to unit stress, a string of any given material and length 
tunes to the same frequency if the unit stress is the same. To say that 
better, as long as the material and unit stress is unchanged, the 
frequency will also be unchanged.

Higher tensions produce louder sounds because the string has more energy 
for the same displacement. A thicker string doesn't in itself produce a 
lower tone. To lower the pitch without making the string too slack, it 
is wound in a way that adds little stiffness and bears little of the 
tension. The wound string has greater tension and is therefore louder 
than an unwound string of the same tension-bearing material and pitch.

jerry
-- 
Engineering is the art of making what you want from things you can get.
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