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© 2000-2019   Gérard P. Michon, Ph.D.

Sound and Acoustics

 Michon
 

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Longitudinal and Transverse Wave Motion:  Animations by  Dr. Dan Russell.

Wikipedia :   Sound

Pitch Shifting (8:53)  by  LA Buckner  &  Nahre Sol  (Sound Field, 2019-04-25).

 
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Sound and Acoustics


Ike (Yahoo! 2008-09-11)   Speed of Sound in the Atmosphere
At q°C,  the speed of sound (in m/s) is roughly  V = 331.5 + 0.607 q
If q decreases by 1°C when the altitude z increases by 150 m, how long does it take for an airplane at 9000 m to be heard at sea level at 30°C ?

As q = 30 - z/150, we have  V = 349.71 - (0.607/150) z

dz/dt   =   -V   =   (0.607/150) z - 349.71   =   z / t0 / z - V0
dt   =   dz / ( z / t0 - V0 )   =   d ( t0 Log | z / t0 - V0 | )
Dt   =  

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 still working on this one...


(2015-02-28)  Isaac Newton 
1643-1727   Sound is  not  an isothermal phenomenon!  
Newton's prediction of the speed of sound was  15.48%  too low.

In proposition 49 of Book II of his Principia (1687)  Sir Isaac Newton (1643-1727)  gave the first analytical determination of the speed of sound and noted a discrepancy of about  15%  between his theoretical prediction and the observed value.  He ventured several explanations but missed the  main  one,  which would be given by  Laplace (1749-1827)  more than a century later,  when the budding science of  thermodynamics  came to the rescue.

Newton was right when he equated the square of the celerity of sound to the ratio of pressure and density variations.  However, he was wrong when he obtained the value of that ratio from an  isothermal  equation of state.  It was  Laplace  who first pointed out  (in 1816)  that the proper relation to use for sound is the  adiabatic  equation of state...

Sound is a rapid disturbance to which a fluid  (or a solid)  must react quickly.  It doesn't do so in the same way it would handle slow perturbations where the local gradient of temperature would have enough time to vanish.

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Speed of Sound  by  Kevin S. Brown  (MathPages).


(2006-12-01)  Simon Laplace 
1749-1827   Speed of Sound in a Fluid 
Sound is the propagation of a  reversible  pressure disturbance.

Common experience indicates that sound of a reasonable amplitude propagates very well in the air, without appreciable losses for all frequencies in the  audio  range.  However, a membrane vibrating at an extremely high frequency is essentially hit randomly by gas molecules and its mechanical energy is thus entirely dissipated thermally, instead of being transmitted as a coherent wave.

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Sound attenuation in the atmosphere
Laplace and the Speed of Sound  by  Bernard S. Finn  (1964).


(2006-12-01)  Johannes van der Waals 
 1837-1923   Speed of sound in a Van der Waals fluid 
The formula applied to the Van der Waals equation of state.

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 still working on this one...

Acoustic cut-off frequency of the Sun & solar magnetic activity cycle  (2011)  by  A. Jimenez, R.A. Garcia, P.L. Palle.


(2006-12-01)   Acoustic Cutoff in the Sun's Atmosphere:  5.3 MHz 

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 still working on this one...

Acoustic cut-off frequency of the Sun & solar magnetic activity cycle  (2011)  by  A. Jimenez, R.A. Garcia, P.L. Palle.


(2006-12-02)   Measuring sound in Decibels  (dB)
Physical measurements and perceived loudness.

Both sound and light can be measured either in abolute terms related to the abolute power (in watts) carried by a wave, or in "human" terms involving a simplified model of the human senses.  For light, the power "perceived" by the retina is measured in  lumens,  not watts.  For a pure color  (single light frequency)  the two are proportional.  The cofficient of proortionalitiy is called the mechanical equivalent of light and is equal to 638 lm/W  (683 lumens per watt)  at 540 THz, by definition of the  lumen.

In the case of sound, one measure of power is the so-called  sound intensity,  which is the physical power flowing through a unit surface.  The SI unit of physical sound intensity is the watt per square meter (W/m).  The amplitude of sound is defined in terms of pressure differences and measured in  pascals (Pa).

From a physical standpoint, sound is best described in terms of the actual  root mean square  (RMS)  flux of the mechanical power` carried by a soundwave, irrespective of the ability or inability of the human ear to gauge it in terms of perceived  loudness.  If that viewpoint is adopted,  then:

0 dB level (SIL)   corresponds to a  sound intensity  of  10-12 W/m2

That convention is preferred by physicists for theoretical computations.

The RMS power of a complicared wave is simply the sum of the RMS powers of all its sinusoidal  harmonic constituents.  Two sine waves of equal amplitude carry the same power even if they have different frequencies.

On the other hand,  a   sound pressure level  (SPL)  of  0 dB  is attributed, by convention, to the barely audible signal corresponding to a peak-to-peak pressure swing of .02 mPa (20 micropascals) in dry air for a a  1 kHz  sine wave.  (For water, the reference pressure swing seems [?] to be 1 micropascal.)  Peak-to-peak measurement cannot be used directly, except for a sine wave.  The power of other signals is the sum of the powers of all their harmonic components  (sinusoidal component).

Another approach exists which may assign  different  loudnesses to two sinusoidal sinewaves of the same amplitude.  This attributes a conventional weight,  closely related to "average" human perception,  to different tonalities.  One common such scale is referred to as dB-A.  Although the dB-A weighing could theoretically be used with the  sound intensity level  (SIL)  defined above,  it's almost exclusively based on the  sound pressure level (SPL)  defined below,  for the simple reason that  sound pressure  is what's actually measured physically  (sound intensity  is deduced).

The two sound scales  (SIL and SPL)  are identical in practice  (up to a tiny shift discussed below)  because the intensity is proportional to the  square  of the sound pressure,  except for  extremely  loud sounds  (which arguably don't even qualify as sound because substantial heat is irreversibly evolved).  Thus,  a 20 dB  increase is  either  a tenfold increase in sound pressure or a hundred-fold increase in sound intensity.

Under ordinary circumstances,  sound pressure  is what's actually measured physically  and  sound intensity  is deduced.

Either way,  the measurement results corresponding to any mix of frequencies can be reported with or without reference to actual human perception.  One common scale  (closely related to some "average" human perception)  is known as  "dB-A".  It's opposed to the "dB-C" scale,  which reports the physical amplitudes of sounds without attempting to approximate the subjective way people perceive  loudness.

Customarily in North America,  "dB-SIL" or "dB-SPL" are used to specify  precise physical measurements  (with dB-C weighing)  whereas "dB-A" refers to human-perceived loudness,  often at a lesser precision.  (The latter differs greatly from the competing standard which purports to achieve the same in metrological conditions).

Unqualified  "dB"  indications usually mean "dB-A" in the  audio  field and "dB-SPL" for very loud sounds,  potentially damaging to human hearing  (see table).

The conversion between the SIL and SPL scales simply entails a small additive shift,  involving the logarithm of the ratio between the power flux and the square of the amplitude,  as discussed below.  The different "A-weighting" of audio frequencies takes  roughly  into account the sensitivity of a "typical" young human hear.  The "dB-A" indication  (sometimes pronounced "dB audio" or "dB acoustic")  bears no direct relation with the physical (RMS) scale when a wide acoustic spectrum is considered.

So, what exactly is the peak-to-peak pressure swing of a 1 kHz sinusoidal soundwave at 0 dB RMS?

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 still working on this one...

Numericana :   Measuring sound in decibels


(2006-12-01)   A ceiling to the loudness of atmospheric "sound"...
Consider a 1 kHz  sine wave  of 0 atm minimum and 2 atm maximum.

By definition, a standard atmosphere (atm) is 101325 Pa.

Of course, a pressure disturbance whose amplitude is 2 atm peak-to-peak would not qualify as "sound".  It would not be small enough to be  reversible  and it's difficult to envision how it could take the shape of a symmetrical wave, let alone a sinusoidal one.  Even if such a large disturbance was sinusoidal to begin with, its 100% swing in relative pressure would entail a nonlinear propagation that would soon distort it beyond recognition.

A pressure swing down to zero could be expected in the most violent nuclear or volcanic explosions.  Realistic nonsinusoidal shapes could possibly carry slightly more power than a sinewave with a zero minimum.  However, the latter still gives a good estimate of the highest mechanical energy which the atmosphere of the Earth can carry away in a "soundlike" way, namely:

194 dB-SPL   =   184 dB-RMS ???

The corresponding computation which follows is a good excuse to examine the exact basis which serves to measure the loudness of sound...  Using the "sound pressure level" (SPL) standard, the sine wave described above has 10132500000 times the amplitude of a 0 dB sound.  It has thus a 200 dB (SPL) magnitude  (more precisely: 200.114 dB).

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(2006-12-01)   Acoustical Limits 
Sound waves have a limited amplitude and frequency range.

...

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