petermc61 wrote: ↑
Mon Oct 02, 2017 1:28 am
All I am saying is that I am unaware of any evidence that the amount of vibration (i.e. volume) you get off the soundboard for a given amount of string vibration increases as the static loading on the soundboard goes up with higher string tension.
The conventional argument goes like this:
The main drive to the guitar top are the transverse vibrations of the string that exert a force perpendicular to the soundboard. As the string oscillates, it changes angle as it approaches the "fixed" point at the saddle. The component "P" of the force perpendicular to the sound board is the tension "T" in the string multiplied by the sine of the change in angle from the rest position, "alpha". So P=T*sin(alpha). If the tension T in the string is doubled (for example) then the force causing the top to vibrate (P) also doubles. So the force driving the soundboard is proportional to the tension in the string.
However, what you hear depends on a whole stack of other things. A doubling of the drive force represents a 3dB change in sound level for the same pluck displacement, which is supposed to be a "just noticeable difference"*. However, with a string of a different tension and likely different diameter, the overtone structure of the string, and hence the harmonic structure of the drive force, will change; which may precipitate a difference in apparent
** loudness due to the non-flat frequency response of the human ear. Further, if the increase in string tension precipitates a change in the geometry of the soundboard (for example, results in more soundboard doming) then the soundboard may end up looking structurally stiffer to small variations in drive force, resulting in less motion and less sound radiation.
So it's not simple. However, my guitars generally get perceptibly louder if I string with higher tension strings, but that's not the case for all guitars.
For those who want "Chapter and verse", Section 1.5 in "Design" (specifically Fig. 1.5-5 in Section 1.5.5) for those who have the books.
* I reckon I can reliably hear a lot less than 3dB change in loudness
** A small increase in high frequency content (for example) can come across as perceptibly louder although the total power in the in signal may be the same or less.