Volume of sound

[Doug Richards]

     Hey all,
     
     I had some random thoughts on string/energy thread.
     
     The energy into the "piano system" is provided by pressing the key.  
     Whether it is a very large piano with more tone or an upright spinet.  
     How much of it gets converted from the key to the ear is the point of 
     interest.
     
     When the key is pressed down, it gives the hammer some maximum 
     velocity (read kinetic energy).  Some of the hammers' kinetic energy 
     is transferred from the hammer to the string.  The rest is of the 
     energy is retained and the hammer "bounces" away from the string.
     
     So now the string has energy to dissipate.  Some of the energy is used 
     to excite the soundboard through the bridge that again gets converted 
     to acoustic energy.  Another part of the energy transfer from the 
     string is transferred to the case, hence the vibration you feel on the 
     rim.
     
     We want sound, Right?
     
     Some "piano systems" sing louder and longer than others.  It was 
     already stated that the concert grand is required to fill the building 
     with sound. BUT, the energy into the system via pressing the key was 
     the same as that spinet in the living room.  So what gives?
     
     The difference can only be one of efficiency.  More kinetic energy 
     from the hammer is transformed into acoustic energy off the 
     soundboard.  On a less efficient "piano system", the energy is 
     dissipated in other ways: case vibrations, downbearing, wood grain and 
     moisture conditions and hammer return velocity (to name a few).
     
     Other random thoughts:
     
     The bigger the soundboard (all other things being equal), the more even 
     the frequency response.  This is even more important for low 
     frequencies.  A very small soundboard can not excite low frequencies 
     well because of the length of the sound wave size compared to the size 
     of the soundboard (besides string lengths).
     
     In regards to the potential energy of a string, if it is broken it is 
     converted into kinetic energy and can travel large distances.  
     Otherwise, the potential energy of the string is the same after the 
     sound has died away as before the hammer hit it.  The only energy out 
     of the string is from the hammer.  The string tension has potential 
     energy and will show by what frequency the string sounds when struck.
     
     I'm sure is it a lot more engineering stuff than you were interested 
     in, but ...  
     
     Comments?
     
     doug
     Quantum Corp.
     drichard@qntm.com
     San Jose, CA
     
     
     
     
______________________________ Reply Separator _________________________________
Subject: Volume of sound
Author:  wtscherer <WallyTS@CompuServe.COM> at SMTP 
Date:    6/5/97 10:58 AM
     
     
Michael,
     
Let's start with the biggest piano available and say that the sound that 
comes from that represents the standard. Assuming that the force of the 
hammer on a smaller piano is the same as our standard, the reason for there 
being less sound, therefore, must be due to limiting factors as compared to 
our standard - shorter strings, smaller soundboard, etc. It's not that a 
larger piano is using up a small amount of potential energy more quickly, 
it's that a smaller piano is limiting a large amount of potential energy.
     
Wally Scherer
Norfolk, VA
WallyTS@compuserve.com