Late added note:

Those conflagration thermal plumes can be expected to be oxygen depleted.

Jets flying through them might stall if their mixture control computers can't compensate and keep up a functional stoichiometric ratio.

Care should be taken to fly higher than all risks.  Beware of an unstable thermocline.

 

*****************

 

 
 
To: DARPA(Matthew Goodman), Greg Raths, Dana Rohrabacher, John Moorlach, website
 
Crafted sound extinguishes fires. A short list of references is added at the end.
Almost everyone has seen video of oil well fires put out with a small dynamite blast.
 
Not willing to fiddle while California burns, while taking a few minutes to increase my caffeine,
I thought of this, because it could be tried immediately, instead of in weeks for the alternative I'm working on.
 
So take note, Ask the FAA, Forest Service, Air Force, aircraft manufacturers and others.
Get reruns of Russia's supersonic bombers dumping phos chek into the backyards of homes they are trying to save.
 
It couldn't hurt to fill the boom with a bomb load of fire suppressant.
 
 
 
DARPA might want in the loop, but experiments shouldn't wait a year for them.
 
All that burning forest includes a lot of the usual byproduct of water.
Explosive decompression creates a lot of ultra rapid cooling,
could mist it, compounded by next couple of jets, nucleating on sucked back soot and smoke,
further isolating fuel from air, wetting and cooling forest fuel.
Consider for breaking up/splitting up firefronts, managing firebreaks,
and emergency stops for pre-burns or trapped vehicles and homes.
 
Frequency, boom, jet spacing  ~50 Hz (30 to 60)
0.02 seconds, 6.864 meters apart, 22.52 feet
seems small, but I've been up for days, double-check please.
 
 
 
 

Equations[edit]

In general, the speed of sound c is given by the Newton-Laplace equation:

c = \sqrt{\frac{K_s}{\rho}},

where

  • Ks is a coefficient of stiffness, the isentropic bulk modulus (or the modulus of bulk elasticity for gases);
  • \rho is the density.

Thus the speed of sound increases with the stiffness (the resistance of an elastic body to deformation by an applied force) of the material, and decreases with the density. For ideal gases the bulk modulus K is simply the gas pressure multiplied by the dimensionless adiabatic index, which is about 1.4 for air under normal conditions of pressure and temperature.

For general equations of state, if classical mechanics is used, the speed of sound c is given by

c = \sqrt{\left(\frac{\partial p}{\partial\rho}\right)_s},

where

  • p is the pressure;
  • \rho is the density and the derivative is taken adiabatically, that is, at constant entropy s.

If relativistic effects are important, the speed of sound is calculated from the relativistic Euler equations.

In a non-dispersive medium, sound speed is independent of sound frequency, so the speeds of energy transport and sound propagation are the same for all frequencies. Air, a mixture of oxygen and nitrogen, constitutes a non-dispersive medium. However, air does contain a small amount of CO2 which is a dispersive medium, and causes dispersion to air at ultrasonic frequencies (> 28 kHz).[5]

In a dispersive medium sound speed is a function of sound frequency, through the dispersion relation. Each frequency component propagates at its own speed, called the phase velocity, while the energy of the disturbance propagates at the group velocity. The same phenomenon occurs with light waves; see optical dispersion for a description

 

Altitude variation and implications for atmospheric acoustics[edit]

Density and pressure decrease smoothly with altitude, but temperature (red) does not. The speed of sound (blue) depends only on the complicated temperature variation at altitude and can be calculated from it, since isolated density and pressure effects on sound speed cancel each other. Speed of sound increases with height in two regions of the stratosphere and thermosphere, due to heating effects in these regions.

In the Earth's atmosphere, the chief factor affecting the speed of sound is the temperature. For a given ideal gas with constant heat capacity and composition, sound speed is dependent solely upon temperature; see Details below. In such an ideal case, the effects of decreased density and decreased pressure of altitude cancel each other out, save for the residual effect of temperature.

Since temperature (and thus the speed of sound) decreases with increasing altitude up to 11 km, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.[6] The decrease of the sound speed with height is referred to as a negative sound speed gradient.

However, there are variations in this trend above 11 km. In particular, in the stratosphere above about 20 km, the speed of sound increases with height, due to an increase in temperature from heating within the ozone layer. This produces a positive sound speed gradient in this region. Still another region of positive gradient occurs at very high altitudes, in the aptly-named thermosphere above 90 km.

The approximate speed of sound in dry (0% humidity) air, in meters per second, at temperatures near 0 °C, can be calculated from

c_{\mathrm{air}} = (331{.}3 + 0{.}606 \cdot \vartheta)~\mathrm{m/s},

where \vartheta is the temperature in degrees Celsius (°C).

This equation is derived from the first two terms of the Taylor expansion of the following more accurate equation:

c_{\mathrm{air}} = 331.3~\mathrm{m/s} \sqrt{1 + \frac{\vartheta}{273.15}}.

Dividing the first part, and multiplying the second part, on the right hand side, by \sqrt{273.15} gives the exactly equivalent form

c_{\mathrm{air}} = 20.05~\mathrm{m/s} \sqrt{\vartheta + 273.15}.

The value of 331.3 m/s, which represents the speed at 0 °C (or 273.15 K), is based on theoretical (and some measured) values of the heat capacity ratio, \gamma, as well as on the fact that at 1 atm real air is very well described by the ideal gas approximation. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas \gamma is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.

This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and for this reason will fail, particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's stratosphere. The equation fails at extremely low pressures and short wavelengths, due to dependence on the assumption that the wavelength of the sound in the gas is much longer than the average mean free path between gas molecule collisions. A derivation of these equations will be given in the following section.

A graph comparing results of the two equations is at right, using the slightly different value of 331.5 m/s for the speed of sound at 0 °C.

Effects due to wind shear[edit]

The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.[6] Wind shear of 4 m·s−1·km−1 can produce refraction equal to a typical temperature lapse rate of 7.5 °C/km.[9] Higher values of wind gradient will refract sound downward toward the surface in the downwind direction,[10] eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.[11]

For sound propagation, the exponential variation of wind speed with height can be defined as follows:[12]

U(h) = U(0) h^\zeta,
\frac{dU}{dH} = \zeta \frac {U(h)}{h},

where

  • U(h) = speed of the wind at height h, and U(0) is a constant;
  • \zeta = exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52;
  • \frac{dU}{dH} = expected wind gradient at height h.

In the 1862 American Civil War Battle of Iuka, an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle,[13] because they could not hear the sounds of battle only 10 km (six miles) downwind.[14]

Tables[edit]

In the standard atmosphere:

  • T0 is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m/s (= 1086.9 ft/s = 1193 km/h = 741.1 mph = 644.0 kn). Values ranging from 331.3-331.6 may be found in reference literature, however;
  • T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m/s (= 1126.0 ft/s = 1236 km/h = 767.8 mph = 667.2 kn);
  • T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m/s (= 1135.6 ft/s = 1246 km/h = 774.3 mph = 672.8 kn).

In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure or density (since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere—actual conditions may vary.

Effect of temperature on properties of air
Temperature
T (°C)
Speed of sound
c (m/s)
Density of air
ρ (kg/m3)
Characteristic specific acoustic impedance
z0 (Pa·s/m)
35 351.88 1.1455 403.2
30 349.02 1.1644 406.5
25 346.13 1.1839 409.4
20 343.21 1.2041 413.3
15 340.27 1.2250 416.9
10 337.31 1.2466 420.5
5 334.32 1.2690 424.3
0 331.30 1.2922 428.0
−5 328.25 1.3163 432.1
−10 325.18 1.3413 436.1
−15 322.07 1.3673 440.3
−20 318.94 1.3943 444.6
−25 315.77 1.4224 449.1

Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

Altitude Temperature m/s km/h mph kn
Sea level 15 °C (59 °F) 340 1225 761 661
11,000 m−20,000 m
(Cruising altitude of commercial jets,
and first supersonic flight)
−57 °C (−70 °F) 295 1062 660 573
29,000 m (Flight of X-43A) −48 °C (−53 °F) 301 1083 673 585
 
 
 
 
 
 
If it works, no water re-loading will be needed to slow the effort..
 
 
 
 
Subject: SonicBoom firefighting
 
 sound blasting fire extinguishment
 
Big sound should have more stopping power than little sound
 
supersonic jet booms spaced for optimum frequency matching.
Someday, adjust dive for best explosive decompression.
Flyby/flythrough afterburners off to avoid adding heat
Shock direction of flight to suck embers/smoke back upwind to cancel embers spread
height AGL above all possible wind/shear updrafts/down drafts.