Mathematics · Mathematical Physics
Free-Field Acoustic Distance Attenuation reference source distance Solver
Rearrange the free-field acoustic distance attenuation relationship and solve for reference source distance.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Use b=a/10^(c/20) with ideal level reduction in decibels=12.041199826559247 and farther source distance=20.
- reference source distance=5.000000000000001.
- Substitution into c=20log₁₀(a/b) reconstructs 12.041199826559245.
Understand Free-Field Acoustic Distance Attenuation: solve reference source distance
One idea, three depths
Choose how deeply to explain Free-Field Acoustic Distance Attenuation: solve reference source distance
Free-Field Acoustic Distance Attenuation: solve reference source distance: Rearrange the free-field acoustic distance attenuation relationship and solve for reference source distance.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Free-Field Acoustic Distance Attenuation: solve reference source distance to answer this question: rearrange the free-field acoustic distance attenuation relationship and solve for reference source distance? Enter ideal level reduction in decibels and farther source distance; the calculator shows reference source distance. For example: farther source distance=20 and reference source distance=5 produce ideal level reduction in decibels=12.041199826559247. The answer tells you reference source distance.
Age 15Explain it to a 15-year-oldConnect it to the formula
For spherical free-field spreading, sound-pressure level reduction between distances is twenty times the logarithm of their ratio. This page isolates reference source distance and verifies it in the original relationship. The rule is b=a/10^(c/20). Its input values are ideal level reduction in decibels, farther source distance, and the main result is reference source distance. For example: farther source distance=20 and reference source distance=5 produce ideal level reduction in decibels=12.041199826559247.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated free-field acoustic distance attenuation: solve reference source distance relation over the valid real-number domain stated below. The implemented relation is b=a/10^(c/20), evaluated from ideal level reduction in decibels, farther source distance to produce reference source distance. For spherical free-field spreading, sound-pressure level reduction between distances is twenty times the logarithm of their ratio. This page isolates reference source distance and verifies it in the original relationship. This excludes reflections, absorption, barriers, source directivity, ground effects, near-field behavior, and changes in source power.
Inputs and valid domain
- ideal level reduction in decibels must be a finite real number.
- farther source distance must be a finite real number.
Important boundary: This excludes reflections, absorption, barriers, source directivity, ground effects, near-field behavior, and changes in source power.
The formula
b=a/10^(c/20)
How the calculator works through it
It substitutes ideal level reduction in decibels, farther source distance into the formula and exposes every numerical step above. The main output is reference source distance, accompanied by Reconstructed ideal level reduction in decibels.
Read the result correctly
The reference source distance is the direct answer to “rearrange the free-field acoustic distance attenuation relationship and solve for reference source distance.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
farther source distance=20 and reference source distance=5 produce ideal level reduction in decibels=12.041199826559247.
Where this model stops being reliable
This excludes reflections, absorption, barriers, source directivity, ground effects, near-field behavior, and changes in source power.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Free-Field Acoustic Distance Attenuation: solve reference source distance works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Free-Field Acoustic Distance Attenuation: solve reference source distance uses b=a/10^(c/20). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Ratios, units and dimensional meaning
Tracking ratios and units keeps the Free-Field Acoustic Distance Attenuation: solve reference source distance result physically interpretable instead of merely numerical.
Review this foundation about 5 min
Optional enrichment
- Vectors and physical direction
Vector language extends Free-Field Acoustic Distance Attenuation: solve reference source distance when magnitude and direction must be treated separately.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Read ideal level reduction in decibels, farther source distance.
- Evaluate the principal relationship: b=a/10^(c/20).
- Return reference source distance and check the domain conditions described above.
Python
from math import *
def free_field_acoustic_distance_attenuation_solve_b(c, a) -> float:
return (a / pow(10.0, (c / 20.0)))
assert abs(free_field_acoustic_distance_attenuation_solve_b(12.041199826559247, 20) - 5.000000000000001) < 1e-6 * max(1.0, abs(5.000000000000001))
C
#include <assert.h>
#include <math.h>
double free_field_acoustic_distance_attenuation_solve_b(double c, double a) {
return (a / pow(10.0, (c / 20.0)));
}
int main(void) {
const double expected = 5.000000000000001;
const double actual = free_field_acoustic_distance_attenuation_solve_b(12.041199826559247, 20);
assert(fabs(actual - expected) < 1e-6 * fmax(1.0, fabs(expected)));
}
C++
#include <cassert>
#include <cmath>
#include <numbers>
double free_field_acoustic_distance_attenuation_solve_b(double c, double a) {
return (a / std::pow(10.0, (c / 20.0)));
}
int main() {
constexpr double expected = 5.000000000000001;
const double actual = free_field_acoustic_distance_attenuation_solve_b(12.041199826559247, 20);
assert(std::fabs(actual - expected) < 1e-6 * std::fmax(1.0, std::fabs(expected)));
}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · SSE2 with libm where required
; double free_field_acoustic_distance_attenuation_solve_b(double c, double a)
; Linux x86-64 NASM · System V ABI · first eight doubles in xmm0–xmm7
extern pow
global free_field_acoustic_distance_attenuation_solve_b
section .text
free_field_acoustic_distance_attenuation_solve_b:
push rbp
mov rbp, rsp
sub rsp, 64
movsd [rbp-8], xmm0
movsd [rbp-16], xmm1
mov rax, 0x4024000000000000
movq xmm0, rax
movsd [rbp-40], xmm0
mov rax, 0x4034000000000000
movq xmm0, rax
movsd [rbp-56], xmm0
movsd xmm0, [rbp-8]
divsd xmm0, [rbp-56]
movsd [rbp-48], xmm0
movsd xmm0, [rbp-40]
movsd xmm1, [rbp-48]
call pow wrt ..plt
movsd [rbp-32], xmm0
movsd xmm0, [rbp-16]
divsd xmm0, [rbp-32]
movsd [rbp-24], xmm0
movsd xmm0, [rbp-24]
leave
ret
MATLAB
function result = free_field_acoustic_distance_attenuation_solve_b(c, a)
result = (a / (10.0 ^ (c / 20.0)));
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[c_, a_] := (a / (10.0 ^ (c / 20.0)));
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
University Physics Volume 3
Read OpenStax University Physics: Quantum MechanicsCite this book
- APA 7
- Ling, S. J., Sanny, J., & Moebs, W. (2016). University physics volume 3. OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction
- MLA 9
- Ling, Samuel J., et al. University Physics Volume 3. OpenStax, 2016, https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
- Chicago author-date
- Ling, Samuel J., Jeff Sanny, and William Moebs. 2016. University Physics Volume 3. Houston, TX: OpenStax. https://openstax.org/books/university-physics-volume-3/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Free-Field Acoustic Distance Attenuation reference source distance Solver. MW SysArc Tools. https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver
MLA 9
MW SysArc. “Free-Field Acoustic Distance Attenuation reference source distance Solver.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Free-Field Acoustic Distance Attenuation reference source distance Solver.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver.
Harvard
MW SysArc (2026) ‘Free-Field Acoustic Distance Attenuation reference source distance Solver’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_free_field_acoustic_distance_attenuation_solve_b_2026,
author = {{MW SysArc}},
title = {Free-Field Acoustic Distance Attenuation reference source distance Solver},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Free-Field Acoustic Distance Attenuation reference source distance Solver
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/mathematical-physics/free-field-acoustic-distance-attenuation-reference-source-distance-solver
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Free-Field Acoustic Distance Attenuation: solve reference source distance do?
Rearrange the free-field acoustic distance attenuation relationship and solve for reference source distance.
How does the Free-Field Acoustic Distance Attenuation: solve reference source distance work?
The calculator applies b=a/10^(c/20). For spherical free-field spreading, sound-pressure level reduction between distances is twenty times the logarithm of their ratio. This page isolates reference source distance and verifies it in the original relationship.
What can I learn from the Free-Field Acoustic Distance Attenuation: solve reference source distance?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .