24 Jun
2011
24 Jun
'11
3:13 p.m.
On Fri, Jun 24, 2011 at 01:58:47PM +0200, Philipp Überbacher wrote:
I found a bit of explanation of wave propagation in
one of my books, but
it seems to differ slightly. It basically takes energy and heat into
account and says (simplified) that there are basically two states, one
without motion but increased pressure and heat, one with maximum motion
and little pressure/heat, and everything in between. I guess this
corresponds to P() and V() in your explanation?
Can't say without seeing your book. P() and V() certainly
are not 'two states', they are two components of a single
state. You can create any combination of P and V at a
given point.
But for a _single source_ they are related, and you
could map them to voltage and current, with the quotient
being the acoustic impedance (as in Ohm's law).
Again, for the P and V fields generated by a single source
at suffient distance, or a plane wave, P and V are in
phase. Their maxima occur at the same points at any time.
It's very common misconception that the energy in a wave
'alternates' between potential energy (at a P maximum)
and kinetic energy (at a V maximum) as it does for e.g.
a pendulum. Even the Wikipedia article on acoustic waves
gets this wrong. In fact the power is proportional to the
product of P and V (as it is to the product of voltage
and current). If the two were 90 degrees out of phase
the average power would be zero.
I guess this sort of analysis or model is used for
more complex systems
like ambisonics as well?
Yes. In ambisonics the P/V ratio, divided by its expected value for
a plane wave (i.e. the acoustic impedance), is called 'rV'. A good
decoder is designed to generate rV = 1 for low frequencies. It's
done by adding an antiphase signal in a direction opposite to the
intended source. This increases the vector sum of V, and decreases
the sum of P, so they can be made to match again.
Ciao,
--
FA