Post by Ken PlotkinOn Sun, 19 Dec 2010 19:01:47 +0100, "Szczepan Bialek"
Post by Szczepan BialekIt is too sophisticated. My question was: "Are speeds of the sound waves the
amplitude dependent?
There will be. But you first have to refine your definition of
"amplitude". Is it displacement? velocity? pressure? temperature?
My study of it explored the pressure aspect. In particular, when a sound
wave travels through air, it creates locales of high pressure and low
pressure, sometimes referred to as "peaks" and "troughs". The peaks are
places where the local instantaneous air pressure is at it greatest for the
wave, while the troughs are places where the air pressure is a minimum for
the same wave at another instant or another place. The acoustic difference
between these two locale types is infinitesimal for most common sound
levels. But when the acoustic pressure becomes comparable to the static
pressure there, the compression tat results from the higher pressure and the
rarefaction causes a half-cycle later will each alter the speed of sound
there. The compression is adiabatic, so the air heats up for these few
microseconds, increasing the sound speed accordingly.
What is observed is different in two frames of reference.
If you choose to ride astride a wave of amplitude greater than about 160
dB (in air) from the source out to a great distance, you will see the
pressure peak advance slowly ahead of the base of the valley behind. After a
few meters, the pressure maximum will abut the base of the valley ahead and
form a plane face, becoming a shock wave. I have not seen measurements of
the speed of this shock wave. Interesting theories can emerge! ANY ONE?
If you choose instead to remain near the source and to browse that
general vicinity, you will see no nonlinearity in the air at and near the
source. But starting at a foot or so out, the pressure waveform as seen by a
pressure microphone will show a bending forward of the crest and a trailing
of the valley. You will also feel a slight breeze, called "sonic wind",
away from the source. (This could be the alternative to a wave speed
uptick.) If the source is a horn-like transmitter, or even just a dipole
like a loudspeaker, you will find that breeze to exist only along and near
the projected beam. That wind will create a velocity profile that will
refract the sound beam outward (like a convex lens) and diminish the sound
beam intensity. That refraction effect, however is easily prevented by
blowing a stream of local air across that beam.
The distance where the wave shape nonlinearity (no longer being a sine
wave) is seen varies from about one to ten feet or more. I'm describing
measurements I made at 15 kHz in air; See JASA, January, 1980). These were
in free air (anechoic).
If the same sound energy was instead captive in a tube or pipe, the
sound level needed to generate the nonlinearity would be less and the
distance in the pipe they would propagate would be much, much greater. There
would also be a small reduction in static pressure at the source end of this
tube, an equivalent for the sonic wind.
I believe that sound pressure inside the pipes of trumpets and trombones
are shock waves by the time they get to the end bell for radiation into
space, possessing the rich harmonics we like so much. The shock formation
process unifies the wave shape so the the timbre is formed by the instrument
and not by the player. The pneumatic pulsing of the player's lips launch
pressure pulses to be sure, but as those waves propagate down the tubes,
they morph into perfect shock waves on heir own via this finite amplitude
effect.
Post by Ken PlotkinIf propagation is nonlinear, it does not shift frequencies in the same
sense as a Doppler shift or the red shift of the cosmos.
Do not think of "frequency" when within a wave. All that is there is in
it is a spatial distribution of pressure.
The first place that there is chance for "frequency" to exist as we
commonly understand (a single perodicity unique in frequency and phase) is
at the position of a stationary ear or microphone. There, the succession of
pressures that exist at that position - if you like; the train of waves
presents it's own pressure, parcel after parcel... The tempo of these
presentations synthesizes the "frequencies". From this point of view, it is
easy to contemplate "Doppler" as being the result of the ear moving around
or the source moving around.......
Post by Ken PlotkinEach portion
of a nonlinear wave propagates at a different speed, dependent on its
local amplitude, so waveforms distort. If you start with a sine wave
of some frequency, then after a while it won't be a sine wave any
more. Not really a frequency shift, but a transfer of energy into
different frequencies - both higher and lower than the original.
That sort of says it, too.
Ange
