[LAU] Where do the 60 degrees for stereo come from?
Fons Adriaensen
fons at linuxaudio.org
Fri Jun 24 13:13:49 UTC 2011
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
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