Boomstick Diagnostics — Technical Reference
Atmospheric Effects on Sound Measurement
Temperature, humidity, barometric pressure, altitude, and wind all enter a firearm sound measurement through known physics. This reference states each mechanism, gives the governing formula with citations, and quantifies what each one is worth at a 1.0 m microphone.
1 Where Weather Enters the Measurement
source · path · receiverA measured peak level is the product of three stages, and the atmosphere acts on all three. Every mechanism in this document belongs to one of them:
- The source — muzzle-blast formation scales with ambient pressure and temperature (Sachs scaling [5][6]), and interior ballistics adds its own term: propellant burn rate is temperature-sensitive, so the same lot leaves the muzzle at a different velocity on a different day.
- The path — the air between muzzle and microphone sets the speed of sound (arrival times, projectile Mach number), the characteristic impedance ρc (pressure produced by a given acoustic power), molecular absorption (frequency-dependent attenuation, ISO 9613-1 [1]), and — outdoors at long range — refraction by wind and temperature gradients [7][8].
- The receiver — measurement microphones carry static-pressure and temperature coefficients (IEC 61094 [10]), and pistonphone-type calibrators require a barometric correction (IEC 60942 [10]).
The organizing fact: most atmospheric terms are common-mode. A suppression result is a difference — bare minus suppressed — taken minutes apart in the same air, on the same host, same ammunition lot, same microphone setup. Path impedance, absorption, and calibration terms appear in both legs with the same sign and largely cancel in the difference. Absolute levels compared across days, sites, or laboratories do not get this protection, which is why each mechanism below is quantified for the absolute case.
2 Summary Assessment
the magnitudes, stated once, for a 1.0 m test geometryWeather moves close-range absolute numbers by fractions of a decibel. Two exceptions are worth watching:
- Altitude — a real effect with a known ceiling of about a decibel and a half at 5,000 ft; the actual shift is usually somewhat smaller.
- Loads near the speed of sound — how much temperature change it takes to flip the signature depends on how close the load already sits to the sound barrier. The barrier moves only about 2 fps per °C, so a load parked near it can flip between a cold morning and a warm afternoon, while one 50 fps away needs a season.
And when two measurements are taken minutes apart in the same air, the atmospheric effects land on both nearly equally — the difference between them is largely protected from the weather, with a leftover expected to be smaller than normal shot-to-shot variation.
For the measurement geometry assumed throughout this document — microphones 1.0 m from the muzzle and at the shooter’s-ear position — the atmosphere is a second-order actor. The propagation path is short enough that the path-dependent mechanisms (absorption, refraction) never accumulate; what remains are the source and impedance terms, stated here as bounds on the absolute peak level:
- Temperature — the largest weather variable, and its main path runs through the ammunition, not the air. The direct acoustic term is the characteristic impedance, worth -0.26 dB across a 0→35 °C span under an equal-radiated-power assumption (Section 3). The indirect terms are larger: propellant temperature sensitivity moves muzzle velocity enough for an estimated 0.1–0.5 dB on an unsuppressed peak (built on the Army-measured temperature coefficient [15] and the measured velocity-to-level slope [12]; cartridge temperature, not air temperature, is the physical variable), and any load whose nominal velocity sits in the 1046–1173 fps window can change sonic regime outright — a signature change no scalar correction describes. Loads well clear of that window, subsonic pistol and supersonic rifle alike, see only the fractional-decibel terms.
- Altitude — the largest single systematic term, entering as a pressure-scaling bound. The pressure-only bound 20 log10(p/p0) evaluates to -1.6 dB at 5,000 ft and -3.3 dB at 10,000 ft; the realized change at a fixed 1.0 m distance lies between that bound and zero, because the Sachs distance rescaling partially offsets the pressure factor (Section 4). The scale of the term is set by the site, so it is reportable rather than random — but it is a ceiling to quote, not an offset to subtract, and the day’s measured station pressure is the correct input, not the standard-atmosphere value. Day-to-day barometric weather contributes only ±0.13 dB about the site mean.
- Humidity — negligible at this geometry. The density and sound-speed terms are hundredths of a decibel, and per-component absorption within the 50 Hz–2 kHz blast band stays under 0.05 dB over 1.0 m in any humidity. The resulting change in a broadband peak has not been separately quantified, but it is bounded by the largest per-component loss across the occupied measurement bandwidth — a fraction of a decibel even including ultrasonic content. Humidity’s real influence — molecular absorption of high frequencies — is a per-distance effect that a 1.0 m path never accumulates; it belongs to bystander-distance and long-range work.
- Comparative results are protected by construction — substantially, not perfectly. Bare-minus-suppressed differences taken within a session share the same air, so the terms above enter both legs with the same sign and largely cancel (Section 1). The residuals that survive the difference are atmospheric second-order effects: frequency-dependent absorption acting on two different spectra, source coefficients that a suppressor can alter, a transonic load crossing Mach 1 in only one leg, and weather drift across a long session. For loads well clear of Mach 1 these residuals are expected to be small at 1.0 m compared with ordinary shot-to-shot spread — an expectation, not yet a separately measured result — and they belong in the uncertainty budget, not at zero by assumption. The bounds in this list apply to absolute levels compared across days, seasons, or sites.
Net assessment. At fixed altitude, an illustrative worst-case linear envelope on an absolute close-range peak — taken about mid-range reference conditions — is ±0.5 dB for a load outside the transonic window (±0.13 impedance + ±0.23 ballistic + ±0.13 barometric + ±0.05 humidity, summed linearly over half-spans about the annual mean — an envelope, not a statistical uncertainty), with the ballistic velocity term the largest contributor — comparable to, or smaller than, ordinary shot-to-shot spread within a string. Two conditions break the generalization: a change of site altitude (a pressure-scaling bound of up to -1.6 dB at 5,000 ft) and a transonic load crossing Mach 1 (Section 3). Same-session comparative results retain an atmospheric residual that, for loads well clear of Mach 1, is expected to be small compared with ordinary shot-to-shot spread — spectrum- and configuration-dependent, and carried in the uncertainty budget rather than set to zero (Section 7).
3 Temperature
speed of sound · transonic flips · impedance · propellantSound travels faster in warm air and slower in cold air. The biggest practical effect is not on the sound but on the bullet: many loads leave the barrel slower when the ammunition itself is cold, and the speed of sound drops with the air temperature — so a load that flies below the speed of sound in summer can cross it in winter and add a sharp ballistic crack that was not there before. The change in the air itself is worth only a fraction of a decibel at close range.
- Speed of sound — in dry air, temperature alone sets it (pressure and density cancel in the ideal-gas form [4]):
- Slope near room temperature — dc/dT = c/2T ≈ +0.59 m/s per °C (1.9 fps per °C); across −20→+45 °C the speed of sound spans 1046–1173 fps.
- Projectile Mach number — M = V/c. Because c moves ≈19 fps per 10 °C, loads in the 1046–1173 fps window change sonic regime with the season: a 1070 fps .22 LR standard-velocity load goes supersonic below -8 °C; a 1150 fps 9 mm 124 gr load goes subsonic above +33 °C. These are air-only crossovers — projectile velocity held at the listed nominal. A ballistic crack appearing or disappearing changes the measured signature far more than any propagation term.
- How much temperature change a flip takes — proportional to the load’s distance from the day’s speed of sound. The boundary moves ≈1.9 fps per °C; for cold-soaked ammunition the propellant term moves the bullet the same direction (≈0.8 fps/°C for a ≈1,100 fps load [15]), so the net closing rate is ≈1.1–1.9 fps per °C. A load 20 fps from the boundary can flip on a 10–15 °C day-to-night swing; one 50 fps away needs a seasonal change. Cold-soaked ammunition therefore crosses at colder air temperatures than the air-only values: if the nominal velocity was established at 20 °C, solving V(Tcartridge)/c(Tair) = 1 with the [15] coefficient moves the 1,070 fps crossover from -8 to ≈-26 °C and the 1,150 fps crossover from +33 to ≈+43 °C — illustrations only, since the real shift depends on the load’s own coefficient and conditioning. For predictions near Mach 1, use chronographed, load-specific velocities and temperature coefficients, not catalog nominals. Right at the boundary the flip is not even binary: ordinary shot-to-shot velocity spread straddles the line, so the crack can come and go within a single string at constant temperature.
- Characteristic impedance — warm air is less dense, so for equal radiated power the same source produces slightly less pressure. The term is 10 log10(ρc/ρ0c0): 0→35 °C at sea level is worth -0.26 dB (Section 4, right panel). This is a conditional linear-acoustic comparison, not a universal blast correction: a constant volume-velocity source would follow 20 log10 instead (≈-0.52 dB), and a muzzle blast is neither pure case — under any source model the term stays below half a decibel.
- Propellant temperature sensitivity — the physical variable is the cartridge’s temperature (propellant, primer, case), for which air temperature is a proxy only once the ammunition has equilibrated outdoors; chamber time and barrel heat move it further. The mechanism is standard interior ballistics: propellant burn rate rises with initial charge temperature, raising chamber pressure and muzzle velocity [16]. The quantitative anchor is a U.S. Army BRL analysis of small-arms data from −65 to +160 °F, which found a fractional muzzle-velocity coefficient of ≈4.1×10−4 per °F for Ball and IMR propellants [15] — about 0.4 fps/°F on a 1,000 fps load and 1.3 fps/°F at 3,240 fps. Some modern powders are formulated for low sensitivity and measure well below that coefficient in published field chronograph tests [17]. Over a 35 °C (63 °F) swing the coefficient gives roughly 26–83 fps across this document’s load range; applying the measured +0.55 dB per 100 fps unsuppressed-baseline slope from [12] (a within-cartridge sweep in which velocity tracked charge energy, so this transfer is an estimate, not a law) puts the interior-ballistics channel at roughly 0.1–0.5 dB — usually the largest temperature effect in the chain, and the least precisely known. Note that a dB-per-fps slope is a local linearization of the underlying energy scaling [12], whose per-fps sensitivity falls as 1/velocity: applying the .22-measured slope at rifle velocities therefore overstates the rifle-end term, which is the conservative direction for an envelope. The slope has been measured only for .22 LR; a second cartridge family would bound it empirically.
Extension to true high-speed rounds (.308, 5.56)
A .308 or 5.56 bullet flies at roughly two-and-a-half to three times the speed of sound, so no weather on Earth can make it subsonic — the crack is always there. Temperature only tunes it: cold air lowers the sound barrier, making the bullet effectively more supersonic, with a slightly stronger crack and a slightly narrower shock cone. Those are small changes — a fraction of a decibel and a few degrees of cone angle across the whole seasonal range. The muzzle blast itself is set by the propellant gases at the muzzle — bullet speed matters mostly as a marker of how much powder energy a load carries, not as the cause of the blast.
- Rifle rounds never flip — a .308 Win at 2,650 fps runs M 2.26 on a +45 °C day and M 2.53 at −20 °C; 5.56 at 3,240 fps spans M 2.76–3.10. No terrestrial temperature brings them near Mach 1 — weather can only modulate how supersonic they are (≈12% across the span, driven almost entirely by c; the propellant term is a second-order assist in the same direction, since cold lowers bullet speed slightly but lowers the speed of sound faster).
- Crack amplitude — the ballistic crack is an N-wave whose peak overpressure follows the Whitham/DuMond scaling below [13][14], with only an eighth-power Mach dependence: for the .308, the entire −20→+45 °C span moves the crack term by just 0.3 dB.
- Crack geometry — the shock-cone half-angle obeys sin θM = 1/M, so the .308’s cone tightens from 26° at +45 °C to 23° at −20 °C. That shifts where and when the crack sweeps a microphone (arrival timing and incidence angle), not the muzzle-blast level.
- The scaling boundary — the +0.55 dB per 100 fps slope [12] is a within-cartridge result: it holds when a faster load in the same family carries more propellant energy. Across cartridges, muzzle-blast level tracks the propellant-gas energy released at uncorking, not projectile velocity, so a .308’s blast cannot be extrapolated from a .22’s slope. The Mach and crack physics above, by contrast, extend cleanly to any velocity.
d = bullet diameter, l = bullet length, r = miss distance (perpendicular distance from the trajectory to the receiver), pa = ambient pressure; slender-body, weak-shock far-field form [13][14]. The crack scales with ambient pressure just as the muzzle blast does; pa cancels in the seasonal Mach-only comparison above.
| Load (nominal) | Velocity, fps | M at −20 °C | M at +20 °C | M at +45 °C | Cone half-angle at +20 °C | Seasonal behavior (air-only, velocity fixed) |
|---|---|---|---|---|---|---|
| 9 mm 147 gr subsonic | 985 | 0.94 | 0.87 | 0.84 | — | subsonic year-round |
| .22 LR standard velocity | 1070 | 1.02 | 0.95 | 0.91 | — | air-only flip at -8 °C |
| 9 mm 124 gr | 1150 | 1.10 | 1.02 | 0.98 | 78° | air-only flip at +33 °C |
| .22 LR high velocity | 1235 | 1.18 | 1.10 | 1.05 | 66° | supersonic year-round — would flip only in +79 °C air, far beyond any weather |
| .300 BLK supersonic 125 gr | 2050 | 1.96 | 1.82 | 1.75 | 33° | always supersonic |
| .308 Win 168 gr | 2650 | 2.53 | 2.35 | 2.26 | 25° | always supersonic |
| .223/5.56 55 gr | 3240 | 3.10 | 2.88 | 2.76 | 20° | always supersonic |
Reading the last column: a load “flips” when the day’s speed of sound crosses its velocity — the flip temperature is where M = 1 exactly. All entries are air-only values: projectile velocity is held at the listed nominal, so the entries isolate what the atmosphere alone does. Real crossovers also move with cartridge temperature (see the closing-rate bullet above) and with the load’s own velocity spread. A flip temperature far outside the −20→+45 °C band means the regime cannot change in real weather: the high-velocity .22 LR entry, for example, would go subsonic only if the air reached about +79 °C (175 °F), because only air that hot carries sound faster than that bullet flies. The figure is stated to show how far beyond outdoor conditions the crossover lies, not because it can occur.
Temperature acts on the bullet before it acts on the sound — most consequentially near Mach 1. The acoustic terms (impedance, absorption) are worth tenths of a decibel; the ballistic terms (sonic-regime flips, propellant sensitivity) are worth whole decibels on transonic loads. True high-speed rounds are the calm end of the spectrum: their regime never changes, and the crack merely sharpens slightly in the cold (0.3 dB and a few degrees of cone angle for the .308 across the full span). This is why test records log air temperature with every string and why ammunition lot and nominal velocity accompany every reported level.
4 Barometric Pressure & Altitude
source scaling · impedance · calibrationThinner air produces a weaker blast: the peak pressure a muzzle blast can generate scales with how much air is there to compress. Moving a test from sea level to a mile-high site can lower the peak by up to about a decibel and a half — that figure is a ceiling on the effect, not an exact deduction, and the real shift is usually somewhat smaller. Ordinary day-to-day barometer swings move things by roughly a tenth of a decibel.
- Blast-source scaling — Sachs [5] showed that blast overpressure ratios are invariant when pressures are scaled by ambient pressure pa and distances by (pa/E)1/3:
- First-order consequence — at a fixed scaled distance the peak overpressure is proportional to ambient pressure, while the dB reference stays fixed at 20 µPa. At fixed physical distance, lowering pa also shrinks the scaled distance, where Φ is larger — the two effects oppose, so the realized change lies between the pressure-only bound and zero [6]. As an illustration, if the applicable stretch of the decay curve behaved as Φ ∝ 1/Z, the 5,000 ft change would be ≈-1.1 dB rather than -1.6 dB. The actual sensitivity depends on the source and the local slope of its scaled-blast curve; Φ is a similarity curve for a source class, not a universal law for every muzzle device.
- Altitude — with the standard atmosphere [9], p(h) = 101.325 (1 − 2.25577×10−5h)5.25588 kPa (h in meters): a 5,000 ft site sits at 84.3 kPa and the pressure-only bound is -1.6 dB relative to sea level. The standard atmosphere is a model: for reducing actual data, the day’s measured station pressure is the correct input. Day-to-day weather is much smaller: a large synoptic swing of ±1.5 kPa moves the bound by ±0.13 dB at sea level (slightly more at altitude, where the same swing is a larger fraction).
- Impedance — ρ = p/(RdT) falls with altitude and rises with cold, moving the 10 log10(ρc) term by the fractions of a decibel shown below. No separate impedance term is added on top of the Sachs bound: the scaling law already contains the ambient medium, and stacking 10 log10(ρc) onto it would double-count.
- Calibration — a pistonphone generates a pressure proportional to ambient static pressure: at 5,000 ft its uncorrected output is low by roughly the same -1.6 dB computed above. Performing a field calibration does not by itself remove this — the user must apply the pistonphone’s barometric correction (its correction barometer or corrected-level table, per IEC 60942 [10]) or use a calibrator with internal pressure compensation; an uncorrected pistonphone calibration bakes the full pressure error into the working sensitivity. Condenser microphones themselves are far less sensitive: static-pressure coefficients of order hundredths of a dB per kPa and temperature coefficients of order thousandths of a dB per °C (IEC 61094 [10], manufacturer-published typical values).
5 Humidity & Molecular Absorption
moist-air density · ISO 9613-1 formula setHumid air is lighter than dry air, not heavier — water vapor displaces heavier oxygen and nitrogen molecules. At one meter the effect on a measurement is too small to see. Humidity’s real role is soaking up high-frequency sound over long distances, and counter-intuitively, very dry air absorbs some frequencies more strongly than humid air does.
- Moist air is lighter, not heavier — water vapor (M = 18.02 g/mol) displaces heavier N2/O2 (M ≈ 28.97 g/mol). Density follows the partial-pressure sum ρ = (p − e)/(RdT) + e/(RvT); at 20 °C, going 0→100% RH changes density by -0.9% and raises the speed of sound by +1.3 m/s (Cramer [4]). The combined impedance effect is -0.022 dB — negligible.
- Where humidity actually matters: absorption — O2 and N2 molecules absorb acoustic energy through vibrational relaxation, and water-vapor collisions set the relaxation frequencies. The dependence is non-monotonic — it does not simply rise or fall as humidity climbs. Instead, absorption climbs to a peak in fairly dry air and then falls again as the air gets wetter, so very dry air absorbs mid-frequency energy more strongly than humid air (right panel below; the terms are defined in Section 8).
- Magnitudes at 20 °C, 70% RH — computed from [1]: 5.0 dB/km at 1 kHz and 118 dB/km at 10 kHz. In this document “blast band” means the energy-dominant region of a small-arms muzzle blast, taken here as 50 Hz–2 kHz; over a 1.0 m path that band loses at most 0.055 dB in any humidity. Content at 10–20 kHz sees roughly 0.1–0.5 dB/m and the ultrasonic tail approaches a decibel per meter (1.3 dB/m at 40 kHz, 50% RH) — so a very sharp peak is rounded slightly more than the band figure alone suggests.
- What a broadband peak actually depends on — a measured peak reflects the full spectrum through the instrumentation bandwidth, not any single frequency. The statements above assume an unweighted (Z) peak from a measurement chain whose bandwidth extends well beyond the blast band; the α(f) formulas below let any specific bandwidth be assessed directly.
Absorption formula set — Bass et al. [3], as adopted in ISO 9613-1 [1]
- Saturation vapor pressure — log10(psat/pr) = −6.8346 (T01/T)1.261 + 4.6151, with T01 = 273.16 K, pr = 101.325 kPa.
- Molar water-vapor concentration — h = hr (psat/pr) / (p/pr) (percent), hr = relative humidity, %.
- Oxygen relaxation frequency — frO = (p/pr) [ 24 + 4.04×104h (0.02+h)/(0.391+h) ] Hz.
- Nitrogen relaxation frequency — frN = (p/pr)(T/T0)−1/2 [ 9 + 280 h exp(−4.170 [(T/T0)−1/3 − 1]) ] Hz, T0 = 293.15 K.
Worked example — 20 °C, 50% RH, 101.325 kPa, f = 20 kHz. psat = 2.337 kPa ⇒ h = 1.153%; frO = 35.4 kHz; frN = 332 Hz; α = 0.524 dB/m — i.e. 0.524 dB over the 1.0 m muzzle path, and that only for the 20 kHz spectral component, not the broadband peak.
Scope note: ISO 9613-1’s primary stated pure-tone range is 50 Hz–10 kHz, 10–100% RH, −20→+50 °C; the standard also supplies the formulas used here for computation over wider ranges. The equation set above is reproduced from its open-literature publication [3], where the model underlying ISO 9613-1 and ANSI S1.26 is documented; the standards are cited as its governing adoptions. All curves, tables, and worked values in this document are original computations from those equations.
6 Wind & Temperature Gradients
convection · refraction · microphone noiseAt one meter, ordinary wind leaves the blast itself essentially unchanged — what it does is shake the microphone. The rumble of air buffeting the diaphragm can contaminate a recording before the shot itself is affected at all. Wind’s real acoustic work happens far downrange, where it bends sound paths and decides whether a distant listener stands in the sound or in its shadow.
- Convection — wind adds vectorially to the propagation speed (c ± U cos θ). At 5 m/s it shifts a 1 m arrival by tens of microseconds and leaves the peak level unchanged to first order; U/c is only ≈1.5%.
- Refraction — wind shear and temperature lapse bend rays: upward in upwind/daytime-lapse conditions (shadow zones), downward downwind and under inversions (enhancement). These effects grow with range and dominate at tens to hundreds of meters [7][8]; over a 1.0 m path they are immeasurably small. They are the main reason distant observers hear the same rifle differently on different days.
- Microphone wind noise — turbulent pressure fluctuations at the diaphragm are the practical wind problem at short range: low-frequency contamination that can corrupt duration-based and energy-based metrics before it ever threatens the peak. Outdoor measurement procedures cap usable wind speeds at single-digit m/s and call for windscreens [11]; gusty conditions also raise shot-to-shot spread.
- Precipitation and fog — direct acoustic effects are second-order [7]; the operational effects (wet gear, unstable mounts, excluded test days) come first.
7 Net Effect at a 1.0 m Microphone
each variable, a representative swing, and what it is worthThe table collects the mechanisms above for a close-range measurement geometry (microphones 1.0 m from the muzzle; an ear-position microphone near the shooter). Entries are for the absolute unweighted peak; duration- and energy-based metrics (A/B-durations, LAeq, sound-exposure quantities) integrate the low-frequency tail and are more sensitive to wind noise than any entry here. Same-session differences cancel most of these terms.
| Variable | Representative swing | Dominant channel | Worth at 1 m, peak |
|---|---|---|---|
| Temperature (acoustic) | 0 → 35 °C | ρc impedance | -0.26 dB (equal-power model) |
| Temperature (ballistic) | 0 → 35 °C | propellant sensitivity → velocity [12] | ≈ 0.1–0.5 dB (via [15] + [12]) |
| Temperature (regime) | crossing Mach 1 | ballistic crack appears/disappears | signature change, not a correction |
| Relative humidity | 20 → 90% at 20 °C | impedance + per-component absorption | ≤ 0.05 dB per component, 50 Hz–2 kHz; broadband-peak change not separately quantified (bounded by in-band loss) |
| Barometric weather | ±1.5 kPa synoptic | source scaling (Sachs bound) | ±0.13 dB |
| Altitude | sea level → 5,000 ft | source scaling (Sachs bound) | up to -1.6 dB (bound; realized shift smaller) |
| Wind | 0 → 5 m/s | microphone wind noise, gust spread | peak ≈ unchanged; LF metrics at risk |
| Receiver: microphone | 0 → 35 °C; sea level → 5,000 ft | temperature / static-pressure coefficients (IEC 61094, manufacturer-typical) | tenths of a dB uncorrected; folded in by same-day field calibration |
| Receiver: pistonphone calibrator | sea level → 5,000 ft | generated level ∝ ambient pressure (IEC 60942) | ≈ -1.6 dB if the barometric correction is not applied; ≈ 0 with the correction or a compensated calibrator |
| Same-session reduction (bare − suppressed) | any of the above | common-mode cancellation | residual expected small — spectrum- and configuration-dependent; retained in the uncertainty budget (loads clear of Mach 1) |
8 Terms & Symbols
every quantity used in the formulas abovec — speed of sound
How fast a pressure disturbance travels through the local air. It sets arrival times and the threshold a bullet must beat to produce a ballistic crack.
c = 331.3 √(T/273.15) m/s — the dry ideal-gas approximation; T in kelvin. ≈1126 fps at 20 °C.
T; T0, T01, pr — the measured variable and its reference constants
T is the measured air temperature — the input that changes from day to day. The others are fixed anchors the formulas measure against, so results from different labs mean the same thing.
T = air temperature in kelvin (K = °C + 273.15); T0 = 293.15 K (20 °C reference); T01 = 273.16 K (triple point of water); pr = 101.325 kPa (reference pressure).
M — Mach number
The bullet’s speed measured in speeds-of-sound. Above 1, the bullet drags its own shock wave — the crack — a separate source from the muzzle blast, though the two signals can overlap at the microphone.
M = V/c, where V is the projectile’s actual local velocity (this document uses nominal muzzle velocities as example values). The M = 1 boundary moves with temperature because c does.
ρ — air density
How much air mass occupies a cubic meter. All else equal, colder or higher-pressure air holds more; hotter, more humid, or higher-altitude air holds less.
ρ = (p − e)/(RdT) + e/(RvT) kg/m³; Rd = 287.06, Rv = 461.50 J/(kg K).
e, psat, hr, h — water-vapor terms
The water vapor actually present, expressed as its partial pressure (e); the saturation vapor pressure (psat) — the equilibrium value e reaches at 100% relative humidity at that temperature; and the same moisture stated as the familiar percentage (hr) or as the share of all air molecules that are water (h).
e = (hr/100) psat; psat from the ISO 9613-1 triple-point form; h = mole fraction expressed in percent: hr(psat/pr)/(p/pr). The vapor pressure e is unrelated to the exponential ex appearing in the α equation.
ρc — characteristic impedance
How hard the air pushes back on a sound source. Denser air turns the same source power into slightly more pressure at the microphone.
Units Pa s/m (rayl); ≈413 at 20 °C, sea level. Level term: 10 log10[(ρc)/(ρc)ref] dB — valid for equal radiated power in linear acoustics; not an independent muzzle-blast correction (Section 3).
Lp, dB — sound pressure level
A logarithmic ratio, not an absolute unit: +6 dB means double the pressure, +20 dB means ten times. The reference point is fixed by convention and never changes with the weather.
Lp = 20 log10(p / 20 µPa). The 20 µPa reference is absolute, so ambient-pressure effects appear in the measured level, not the reference.
ppk, pa, E, R, Φ — Sachs blast scaling
The peak a blast can produce scales with the ambient pressure it forms in — thin air, weaker blast. Φ is the similarity curve that properly scaled blasts of a given source class collapse onto — one curve per class of source, not one universal curve for every muzzle device.
ppk/pa = Φ[R (pa/E)1/3]: ppk = peak overpressure, pa = ambient pressure, E = source energy, R = distance.
p(h) — standard atmosphere
The internationally agreed model of how pressure falls as a site gets higher — a reproducible reference, not the actual pressure on test day. For reducing real data, use the measured station pressure.
p(h) = 101.325 (1 − 2.25577×10−5h)5.25588 kPa, h in meters (ISO 2533).
frO, frN — relaxation frequencies
The frequencies at which oxygen and nitrogen molecules are best at stealing acoustic energy. Water vapor moves both, which is how humidity controls absorption.
In Hz, from the ISO 9613-1 expressions in Section 5; frO ranges from a few kHz in very dry air to tens of kHz at ordinary humidity; frN sits at hundreds of Hz under ordinary conditions.
α — absorption coefficient
How many decibels a single frequency loses per meter of air. Tiny at close range and low frequency; over long paths it strips the high frequencies first, which is why distant gunfire arrives as a dull thump — both the blast and the crack (which is emitted all along the bullet’s path, not at the muzzle) are rounded and softened en route.
dB/m (often quoted per km), from the ISO 9613-1 equation in Section 5; loss over a path of length x is α·x.
monotonic / non-monotonic
A monotonic relationship moves in one direction only — turn the knob up and the result always goes the same way. A non-monotonic relationship changes direction along the way: absorption first rises as humidity climbs from bone-dry, peaks, then falls as the air gets wetter — so “more humid” can mean either more or less absorption depending on where you start.
A function is monotonic over a range if it is entirely non-decreasing or entirely non-increasing there; non-monotonic if its slope changes sign. α(h) at fixed frequency peaks where the shifting relaxation frequencies pass through that frequency (Section 5, right panel).
θM, d, l, r — ballistic-crack terms
The shock cone’s half-angle, and the bullet dimensions and near-miss distance that set how strong the crack is when it reaches a listener. Faster bullet: narrower cone and — through only a weak eighth-power dependence — a slightly stronger crack.
sin θM = 1/M; Δpcrack/pa ≈ 0.53 d (M²−1)1/8 / (l1/4r3/4), d = bullet diameter, l = length, r = miss distance, pa = ambient pressure; slender-body weak-shock form (Whitham; DuMond et al.). θM is distinct from the wind angle θ.
U, θ — wind terms
Wind speed and its angle to the path between source and microphone. Sound rides the wind: a little faster downwind, a little slower upwind.
Effective propagation speed = c ± U cos θ; refraction at range follows the vertical gradients of the same quantities.
9 References
standards first, then literature- [1] ISO 9613-1:1993, Acoustics — Attenuation of sound during propagation outdoors — Part 1: Calculation of the absorption of sound by the atmosphere.
- [2] ANSI/ASA S1.26-2014 (R2024), Methods for Calculation of the Absorption of Sound by the Atmosphere.
- [3] Bass, H. E., Sutherland, L. C., Zuckerwar, A. J., Blackstock, D. T., Hester, D. M., “Atmospheric absorption of sound: Further developments,” J. Acoust. Soc. Am. 97(1), 680–683 (1995) (article); Erratum, J. Acoust. Soc. Am. 99(2), 1259 (1996); extending Bass, H. E., et al., “Atmospheric absorption of sound: Update,” J. Acoust. Soc. Am. 88(4), 2019–2021 (1990). The absorption equation set used in this document is published in these papers and adopted by [1] and [2].
- [4] Cramer, O., “The variation of the specific heat ratio and the speed of sound in air with temperature, pressure, humidity, and CO2 concentration,” J. Acoust. Soc. Am. 93(5), 2510–2516 (1993) (doi:10.1121/1.405827).
- [5] Sachs, R. G., The Dependence of Blast on Ambient Pressure and Temperature, BRL Report No. 466, Aberdeen Proving Ground, MD (1944).
- [6] Kinney, G. F., Graham, K. J., Explosive Shocks in Air, 2nd ed., Springer-Verlag (1985).
- [7] Embleton, T. F. W., “Tutorial on sound propagation outdoors,” J. Acoust. Soc. Am. 100(1), 31–48 (1996) (doi:10.1121/1.415879).
- [8] ISO 9613-2:2024, Acoustics — Attenuation of sound during propagation outdoors — Part 2: Engineering method for the prediction of sound pressure levels outdoors. Cited only for general refraction phenomenology; the standard is an environmental-noise method and excludes blast sources — [7] is the primary support here.
- [9] ISO 2533:1975, Standard Atmosphere.
- [10] IEC 61094-1 / 61094-4, Measurement microphones (laboratory-standard and working-standard microphone specifications, including environmental coefficients); IEC 60942:2017, Electroacoustics — Sound calibrators (barometric correction for pistonphone-type calibrators; some instruments compensate internally).
- [11] ANSI/ASA S12.18-1994 (R2023), Procedures for Outdoor Measurement of Sound Pressure Level (see also ANSI/ASA S12.7, measurement of impulse noise); MIL-STD-1474E w/ Notice 2 (2025), Design Criteria Standard: Noise Limits — meteorological documentation requirements for reported data.
- [12] Boomstick Diagnostics, Ammunition Velocity Effects Study, SR-001 Rev. A (July 2026) — a within-cartridge .22 LR sweep: one host and one suppressor, nine loads spanning 835–1,640 fps nominal, 46 bare and 90 suppressed shots. The +0.55 dB per 100 fps figure used in Sections 2, 3, and 7 is that study’s unsuppressed shooter’s-ear peak fit; velocity varied with the load, so it tracks charge energy within the family.
- [13] Whitham, G. B., “The flow pattern of a supersonic projectile,” Commun. Pure Appl. Math. 5(3), 301–348 (1952) (doi:10.1002/cpa.3160050305).
- [14] DuMond, J. W. M., Cohen, E. R., Panofsky, W. K. H., Deeds, E., “A determination of the wave forms and laws of propagation and dissipation of ballistic shock waves,” J. Acoust. Soc. Am. 18(1), 97–118 (1946) (doi:10.1121/1.1916347).
- [15] Wagoner, B. A., Change in Muzzle Velocity due to a Change in Propellant Temperature for Small Arms Ammunition, BRL-MR-3825, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD (1990); DTIC ADA221155 — fractional muzzle-velocity temperature coefficient ≈4.05×10−4/°F (Ball and IMR propellants, −65 to +160 °F data).
- [16] Carlucci, D. E., Jacobson, S. S., Ballistics: Theory and Design of Guns and Ammunition, 3rd ed., CRC Press (2018) — interior-ballistics treatment of initial propellant temperature, burn rate, and muzzle velocity.
- [17] “Powder Temp Stability: Hodgdon Extreme vs. IMR Enduron”, PrecisionRifleBlog.com (2016) — published field chronograph measurements of temperature-stable rifle powders (e.g., ≈25 fps over a 115 °F swing for one load); empirical field data, not a standard.
Formulas in Sections 3–5 are reproduced from the cited sources, and the atmospheric quantities in this document are computed directly from those formulas at the stated conditions. Empirical inputs — nominal load velocities, the propellant temperature coefficient [15], the measured velocity-to-level slope [12], field powder-stability data [17], and typical instrument coefficients — are identified as such where they appear.
Revision History
claim-level changes; computed values unchanged throughout- Initial edition (August 2026) — mechanisms, formulas, and magnitudes for the 1.0 m geometry; plain-terms track; glossary; extension to high-velocity rifle rounds.
- Revs. F–G — response to two independent technical reviews: the altitude figure restated as a pressure-only bound rather than an offset; the impedance term conditioned on its source model; the same-session cancellation claim qualified; the ballistic-crack scaling completed with ambient pressure; the propellant temperature coefficient anchored to the Army measurement [15].
- Revs. H–K — the internal velocity study given its citable designation (SR-001) [12]; transonic flip sensitivity quantified; the caliber scope of the velocity-to-level slope stated; the absorption equations anchored to their open-literature publication [3].
- Rev. L — response to a third independent review: sonic crossovers labeled as air-only values with cartridge-compensated illustrations; the pistonphone barometric-correction requirement corrected; the broadband-peak humidity claim scoped to the computed band; references linked; page navigation and mobile metadata added.
© 2026 Boomstick Diagnostics, LLC. All rights reserved. This document — its figures, analysis, and format — is the proprietary work product of Boomstick Diagnostics, LLC and may not be reproduced or redistributed, in whole or in part, without written permission. Third-party data cited herein remains the property of its respective owners and is used with attribution.