Frequency Absorption Calculator

Calculator

Choose a method: use power balance when you know incident, reflected, and transmitted power, or use attenuation when power decays along a path.

Frequency

Used directly and for power-law μ.

Method

Select the model matching your measurements.

Incident power (W)

Total power entering the system.

Reflected power (W)

Set zero if unknown.

Transmitted power (W)

Set zero if blocked/unknown.

Optional notes

Saved into CSV/PDF exports.

Path length

Used in P(x)=P0·e^−2μx.

Attenuation mode

Pick based on available material data.

μ (Np/m)

Use published values when available.

a (coefficient)

μ = a · f^b, with f in Hz.

b (exponent)

Commonly between 0.8 and 2.0.

a unit note

For documentation in exports.

Reset

Example data table

These examples show both supported calculation paths.

Case	Frequency	Method	Key inputs	Key outputs
1	1000 Hz	Power balance	Pi=50 W, Pr=10 W, Pt=25 W	Absorbed=15 W, Coefficient=0.30
2	2 MHz	Attenuation	Pi=10 W, x=0.25 m, μ=3 Np/m	Pout≈2.23 W, Absorbed≈7.77 W
3	500 kHz	Power-law attenuation	Pi=5 W, x=0.10 m, a=1e-12, b=2	μ=0.25 Np/m, Absorbed≈0.24 W

Formula used

Power balance absorption: P_abs = P_i − P_r − P_t
Absorption coefficient (fraction): A = P_abs / P_i
Path attenuation model: P(x) = P₀ · e^−2μx
Absorbed fraction along a path: A = 1 − e^−2μx
Power-law coefficient model: μ = a · f^b (with f in Hz)
Loss in decibels from power ratio: L = 10·log₁₀(P₀/P(x))

Note: μ here is an attenuation coefficient in nepers per meter. If your reference uses different conventions, convert before input.

How to use this calculator

Enter frequency and select its unit.
Pick Power balance if you measured reflected or transmitted power.
Enter incident power, then fill reflected and transmitted as available.
Pick Attenuation
Choose direct μ, or use the power-law μ = a · f^b.
Press Calculate to see results above the form.
Use CSV or PDF buttons to export the latest calculation.

Frequency absorption guide

1. Absorption as an energy budget

Absorption is the portion of incident wave power converted into heat or internal losses. In power balance mode the calculator uses measured incident, reflected, and transmitted power to compute absorbed power and an absorption coefficient. A passive setup yields a coefficient between 0 and 1.

2. Why frequency changes the outcome

Many materials absorb more strongly at higher frequency because frictional and relaxation processes occur more often per second. For acoustics, porous foams show rising absorption from hundreds of hertz into kilohertz bands. For electromagnetics, dielectric loss can grow with frequency depending on conductivity and polarization behavior.

3. Attenuation along a path

When you cannot measure reflected and transmitted power separately, attenuation mode estimates absorption from exponential decay along distance. The model uses P(x)=P0·e^−2μx, where μ is the attenuation coefficient in Np/m. Doubling the path length doubles the exponent term, increasing loss quickly.

4. Converting between nepers and decibels

Engineers report loss in decibels. For power ratios the calculator uses L=10·log10(P0/Px). If you prefer amplitude loss, remember that 1 neper corresponds to about 8.686 dB for amplitude, and about 17.372 dB for power over the same exponent convention, so confirm the definition used in a data sheet.

5. Power‑law μ for broadband studies

Across a wide band, attenuation is approximated by μ=a·f^b. The exponent b captures how rapidly loss rises with frequency; values near 1 indicate roughly linear growth, while b near 2 indicates a faster, quadratic‑like rise. Always input frequency in hertz to keep units consistent.

6. Interpreting coefficients and edge cases

If the power balance produces negative absorbed power, it usually means measurement uncertainty, calibration drift, or a gain element in the path. Likewise, coefficients above 1 indicate inconsistent inputs. Use the “Check” note to flag these cases, then re‑measure reflected and transmitted power or verify instrument averaging and bandwidth settings.

7. Practical data you can log

For repeatable testing, record temperature, humidity, sample thickness, and path length for each run. In many acoustic labs, absorption coefficients are reported at octave‑band center frequencies such as 125, 250, 500, 1000, 2000, and 4000 Hz. In RF work, log frequency, cable length, connector type, and termination quality.

FAQs

1) What is the absorption coefficient in this tool?

It is the absorbed power divided by incident power. In power balance, absorbed power equals incident minus reflected minus transmitted. In attenuation mode, the fraction is 1 − e^−2μx.

2) Why can my absorption fraction be negative?

Negative absorption happens when reflected plus transmitted exceeds incident. This is usually measurement error, mismatched averaging windows, calibration drift, or an active amplifier in the path. Recheck sensor alignment and reference levels.

3) What does μ (Np/m) represent?

μ is an attenuation coefficient that controls exponential power decay with distance. Larger μ means faster loss per meter. If your source provides loss per centimeter or per megahertz, convert it to Np/m before entering.

4) How do I use the power-law option?

Enter a and b so μ = a·f^b, with frequency in hertz. The calculator computes μ at your chosen frequency, then applies P(x)=P0·e^−2μx. Use it for broadband fits.

5) Is attenuation the same as absorption?

Attenuation is overall reduction along a path, which may include absorption, scattering, and leakage. The model here treats that reduction as effective absorption in the medium. For systems with strong reflections, prefer power balance measurements.

6) What inputs should I save for repeatability?

Save frequency, units, incident power, path length, μ or (a, b), and setup notes like temperature and sample thickness. These factors can shift loss significantly between tests, especially at high frequencies.