Why is an Acoustic Guitar so much LOUDER than an Electric Guitar?

[Bob Smith]

Can anyone see how this applies to the acoustic guitar example?

Mile High,
The rod's response to forced resonance is similar to the response of a decent guitar made from solid tone woods. A solid back, sides and top -and neck- will all resonate together, much like your rod example, until the resonance eventually subsides below the audible level.  Cheap guitars made with plywood back, sides, top and neck generally won't resonate this way.
Bob

[MileHigh]

Hey Bob,

You are right and I will throw in lots of colour commentary.

The string is a resonator, the mass of the string per unit length is the capacitance, and the springiness or stretchability of the string is the inductance.

The air cavity is a resonator, where the mass of the air in the hole is the capacitance and the rest of the air inside the cavity acts like a compressible spring so that is the inductance.

Then the main body of the guitar is a resonator where the mass of the wood is the capacitance and the stiffness of the wood is the inductance.

So when you pluck a string, the initial energy in the string resonator starts being coupled to the resonators of the air cavity and the body of the guitar.  They look sort of like electrical transformers, and some of the initial vibrational string energy is coupled or transferred into the other two resonators with a certain coupling factor that is dependent on the frequency.

To be a bit more precise, the string is the driving source of the energy after it gets plucked and the other to resonators simply react, and act like filters.  In other words, the natural resonant frequencies of all three resonators are different.  So it depends on what note the string is playing to see how much the air and guitar body "filters" react to the stimulation.

In the end, you can cut the energy that your finger initially imparted into the string into two things, sound energy and heat energy.  Ultimately the sound energy becomes heat energy also.  Even the string itself heats up as you play it, there is some energy lost in the wire just like bending a coat hanger.

So you pluck the string, and after 10 seconds, all that you are left with is heat.  The resonance was just storing the energy for a short while, and it bleeds off and becomes heat.

MileHigh

[The Observer]

Hey Mile High,

As far as I can tell, you have some decent knowledge when it comes to how resonant systems work.

The most important points that I am trying to impart to others are.

       1, What a Driven or Forced Resonant System is...
            (Small Giver of Energy ------> Receiver of Energy)

       2. How the Receiver in a Forced Resonant Situation receives and STORES ENERGY.

       3. How the Receiver of Energy vibrates at an amplitude congruent to it's STORED ENERGY.

       4. We FEEL/SEE/HEAR the vibrations that are the amplitude of the STORED ENERGY.

                         I would like you to respond to my guitar experiment.

In Summary... While the High E String vibrates for 6 seconds alone,
              the High E will start the Low E and A vibrating (if not damped)
                                                                           and all will ring for 12 seconds !

         If you wanna calculate Watts-seconds using...   Power=Intensity*Area*Seconds

         It is easy to see there is twice the energy ,and that's if it isn't louder... (which it is).

Have a nice day,
                           The Observer

[MileHigh]

The Observer:

While the High E String vibrates for 6 seconds alone,
              the High E will start the Low E and A vibrating (if not damped)
                                                                           and all will ring for 12 seconds !

This is very similar to the string coupling it's energy to the air cavity and the body of the guitar.  In this case it's going from string to string.  I am not a guitar player buy are the High E and the Low E one octave apart?  If yes, then the Low E probably vibrates at it's first harmonic; the High E again.

The bottom line is that the energy drain to heat is slower.  Some of the energy moved over to some other strings, and that ended up extending the life of the oscillations.  From another viewpoint, you simply drained the power out of the oscillation more slowly, producing heat more slowly.

It may appear to sound louder because your ear is so sensitive to sound and you are dealing with the psychoacoustics of how you respond to the apparent volume of two strings vibrating at the same time.

MileHigh

[The Observer]

Hello Mile High,

Thankyou for your response.

I agree that the other strings are vibrating at Harmonics of the High E.

But you say

   

The bottom line is that the energy drain to heat is slower. 
   Some of the energy moved over to some other strings,
    and that ended up extending the    life of the oscillations. 
   From another viewpoint, you simply drained the power out of the
   oscillation more slowly, producing heat more slowly.

Heat drain is slower?

    Come on... You will need to provide something vaguely specific here.

Energy moved over to the other strings?

    Well yes and no.
            Yes....Sound waves crossed the other strings and started them vibrating.
            No... No more energy left the Low E String to accomplish this !
                    (unless you count the energy coming back from all the resonators)

Drained power out of the oscillation more slowly?

        Well, since the Resonators not struck... The Body of the Guitar... the Air in the Guitar,
             the Low E String and the A string... started vibrating..

                       They give off vibrations !!!
     
                             Yes it's true.
   
        And reinforce the system of aforementioned Resonators including the High E. 

                                       This is how it is working... is it not?

Finally, I had to look up psychoacoustics.

     You are saying that I am imagining that it is louder when all 3 strings vibrate.
     I say, yep, just like I imagine that the Acoustic Guitar is louder than an Electric.

Which brings me to my final point.

You say the human ear is sensitive?
   
       I would like to know how in God's good name you figure that?

Did you know the energy difference between 20 and 40 decibels is not 2 times more but 1000 times more.
In other words..  Normal conversation is over 1000 times louder than the library !

My point is... our ears are not sensitive, they need to be UNsensitive to cover the range of volume that they do.

          My next post will include a College Text Book Proof that the waves emitted from an Acoustic Guitar
                            are indeed 1000 times more Powerful than those from an Electric Guitar.

                                                                     The Observer