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Mass law transmission loss

Get a first figure for how well a single wall stops sound: a 10 kg/m² panel at 500 Hz gives about 31.603985401312 dB of transmission loss at normal incidence, plus the share of sound that still passes. Free in your browser.

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Worked example

If you enter

Surface mass: 10
Frequency: 500

You get

Surface mass unit: kg/m²
Frequency unit: Hz
Incidence: normal
Transmission loss db: 31.6039854013

The acoustic mass law is the first-order estimate every acoustician reaches for when a single solid partition must block airborne sound and only surface mass and frequency are known. It describes the inertia-controlled region of an infinite or large panel: heavier walls and higher frequencies raise transmission loss roughly six decibels per doubling of mass or frequency, until stiffness, coincidence, and flanking paths dominate. This mass law transmission loss calculator accepts surface mass in kilograms per square metre and frequency in hertz, optionally chooses normal or field incidence, and returns transmission loss in decibels plus the linear transmission coefficient. Normal incidence uses the physical form with air density and sound speed; field incidence uses the common engineering rule of thumb for diffuse rooms.

What the acoustic mass law predicts for a single partition

Sound transmission loss of a partition is ten times the base-ten logarithm of the reciprocal of the intensity transmission coefficient: TL equals ten log ten of one over tau, expressed in decibels. In the mass-controlled region—well above the panel’s fundamental resonance and below the critical coincidence frequency—the partition behaves primarily as a limp mass.

For normal incidence on an infinite panel the classical result is tau approximately equal to two rho c over omega m, all squared, where omega is two pi f, m is surface mass, and rho c is the characteristic impedance of air. Taking the logarithm yields TL equal to twenty log ten of omega m over two rho c, which rearranges cleanly to TL equals twenty log ten of pi m f over rho c.

With dry air near twenty degrees Celsius, rho is about one point two zero four kilograms per cubic metre and c about three hundred forty-three metres per second, so the constant term is close to forty-two decibels and many handbooks quote TL approximately twenty log ten of m f minus forty-two. Real rooms present a diffuse field rather than a single normal plane wave, so building-acoustics practice often uses a field or random-incidence mass law of the form TL equals twenty log ten of m f minus forty-seven.

Both forms capture the same physics: each doubling of surface mass or frequency adds about six decibels of TL in the mass-controlled band. Neither form includes finite-panel modal behaviour, damping, cavities, or flanking; they are first estimates for a single leaf, not a substitute for laboratory R or field DnT measurements when compliance matters.

What you can do with it

Classroom and homework checks

Let students submit surface mass and frequency and verify mass-law TL (normal or field) against textbook worked examples and the six-decibel-per-doubling rule.

Early design material ranking

Compare candidate single-leaf partitions by estimated TL at octave-band centres when only area density is known, before commissioning laboratory R tests.

Exam and LMS auto-grading

Mark mass-law TL items with a deterministic oracle that rejects non-positive m or f and returns stable rounded decibel values for grading scripts.

FAQ

What is the difference between normal and field incidence?

Normal incidence assumes a single plane wave perpendicular to the panel (physical form with ρ and c).

When is the mass law a poor estimate?

Near panel resonance, near and above the critical coincidence frequency, for double walls with cavities, or when flanking paths dominate. Use laboratory R or field measurements when compliance or detailed design is required.

How much does doubling the mass of a wall improve sound insulation?

About six decibels in the mass-controlled range. Doubling the frequency adds roughly the same amount, until stiffness, coincidence or flanking paths start to dominate.

What transmission loss does a 10 kg/m² panel give at 500 Hz?

About 31.603985401312 dB at normal incidence, with a transmission coefficient of 0.000691196388. Field incidence, typical of real rooms, gives a lower estimate.

What does the transmission coefficient tell me?

It is the fraction of sound intensity that gets through the partition. Transmission loss in decibels is ten times the base-ten logarithm of one over that fraction.

Related tools

For developers — API access

Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.

API endpoint

POSThttps://api.kit.forhosting.com/optics/mass-law-transmission-loss

Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.

Call it from your stack

curl -X POST https://api.kit.forhosting.com/optics/mass-law-transmission-loss \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"surface_mass":10,"frequency":500}'

const res = await fetch("https://api.kit.forhosting.com/optics/mass-law-transmission-loss", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "surface_mass": 10,
    "frequency": 500
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/optics/mass-law-transmission-loss",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "surface_mass": 10,
    "frequency": 500
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/optics/mass-law-transmission-loss", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"surface_mass":10,"frequency":500}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"surface_mass":10,"frequency":500}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/optics/mass-law-transmission-loss", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "surface_mass": 10,
  "frequency": 500
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "optics.mass_law_transmission_loss",
  "status": "queued",
  "_links": {
    "result": "/tasks/tsk_…/result"
  }
}

The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.

Pricing

Per request$0.002

Published price — no tokens, no invented credits. A failed task is never charged.

Errors

HTTP	Code	Meaning
`401`	`unauthorized`	Missing or invalid API key.
`402`	`insufficient_balance`	Your balance doesn't cover the task price.
`404`	`unknown_type`	That task type doesn't exist.
`429`	`rate_limited`	Too many requests. Use the webhook instead of polling.

Technical notes

Input contract, response shape, and validation rules

Optional incidence may be normal or field; when omitted the calculator defaults to normal incidence and evaluates TL equals twenty log ten of pi m f over rho c. Air density and sound speed are always echoed for transparency. Pin the rounded TL and tau fields in automated tests so goldens stay stable across runtimes. POST a JSON body with two required finite positive numbers: surface_mass in kilograms per square metre and frequency in hertz. Aliases such as m, surface_density, area_density, f, freq, and frequency_hz are accepted so clients can match textbook notation without remapping fields. Optional air_density and sound_speed override the default dry-air constants for normal incidence only; field incidence ignores those constants and applies the engineering formula TL equals twenty log ten of m f minus forty-seven. Missing fields, empty strings, non-numeric text, NaN, Infinity, and non-positive mass or frequency fail with invalid_input naming the field. On success the body echoes cleaned surface_mass and frequency with units, reports incidence, transmission_loss_db with transmission_loss_unit equal to dB, transmission_coefficient tau equal to ten to the power of minus TL over ten, formula, message, and ordered steps so you can show the derivation next to the answer. Example: surface_mass equals ten kilograms per square metre and frequency equals five hundred hertz under normal incidence yields a positive TL in the mid twenties of decibels with default air constants; switching incidence to field applies the minus-forty-seven engineering form for a comparable room estimate. Failed validation is not billed; every successful call uses the published $0.002 base price with no model tokens and no outbound network.

Where a mass-law transmission loss API earns its keep

Classrooms and tutoring platforms use a mass law transmission loss calculator so learners can check homework that asks for TL from m and f without mis-counting the constant term or confusing normal with field incidence. Product and HVAC engineers sketch rough airborne insulation of panels, housings, and ducts when only density and thickness—or a catalogue area density—are known. Document that the estimate applies only in the mass-controlled region, keep requests small, and you get reproducible first-order sound insulation numbers for homework, LMS plugins, and edge workers without standing up a full building-acoustics solver of your own. Exam generators need a deterministic oracle that rejects non-positive inputs as invalid_input instead of inventing a decibel value. Architectural and mechanical design notebooks often compare candidate single-leaf materials by surface mass at octave-band centre frequencies before investing in full sound-transmission-class laboratory data; a tiny parse API returns reproducible TL estimates for ranking options.

Technical questions

How do I estimate transmission loss with the acoustic mass law?

For normal incidence use TL = 20·log10(π·m·f/(ρ·c)) with m in kg/m² and f in Hz. For field/random incidence the common engineering form is TL = 20·log10(m·f) − 47. This calculator evaluates either form and returns TL in dB.

What inputs does the mass law transmission loss calculator need?

Two required positive finite numbers: surface_mass (kg/m²) and frequency (Hz). Optional incidence is "normal" (default) or "field". Optional air_density and sound_speed override default dry-air constants for normal incidence.

What does the mass law transmission loss calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →

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