Acoustics Lecture 4

Cornell University Ergonomics Web

DEA3500: Ambient Environment: Building Acoustics

REDUCING BUILDING NOISE: SOUND ABSORPTION

When sound energy hits material, part is reflected, part gets absorbed (part may get transmitted as well). Most materials both reflect and absorb sound.

Absorption coefficient (a) - basically ratio between absorption of a material and open window!

a = Ia / Ii where Ia = sound power density (intensity) absorbed by material (w/cm2) Ii = intensity impinging on material (w/cm2). i.e. - total sound power density.

When a = 1.0 all sound energy is absorbed.

(Note in NRC, a specified at each mid-value of octave bands 250, 500, 1000, 2000.)

Total surface absorption (A) is proportional to area and a value.

A = Sa

where A = total absorption in sabins (named after physicist Sabine)
S = surface area (m2)
a = absorption coefficient

1 Sabin (m2) is the sound absorption equivalent to an open window of one square meter (1 ft2). 1 sabin (m2) = 10.76 sabins (ft2).

Since most rooms are constructed of several materials with different a, total room absorption is sum of components.

i.e. SSa = S1a1 + S2 a2 + S3a3 ....Snan
= SA = A1 + A2 + A3 ....An
where S = area of each material, a = absorption coefficient, A = total absorption of each different material.

Difference between a room with total absorption = 0.1 and same room with total absorption of 0.7 is 15 db i.e. decreased 1.5 x in loudness.

Reverberation - persistence of sound after this has stopped. Consequence of reflections e.g. echoes.

Reverberation Time (Tr) - period required for sound level to decrease 60 dB after sound source has stopped producing sound. For most normal rooms, TR = K x V/ SA where K = constant (0.05 when in feet; 0.16 when in meters), V = room vol. (ft3 or m3), 嫂 = total absorption (sabins (ft2 or m2) at frequency of sound).

TR usually calculated at 125, 500, 1000, 2000 Hz. For speech, 500-1000 Hz range is taken as reference for TR. For music, want to increase reverberation time. For speech, want to decrease reverberation time.

Sound Fields

The inverse square law holds true for the Far field - i.e. open space, but enclosed spaces may behave differently.

Sound at any point in a room is combination of direct sound from source and reflected sound from walls etc. If surfaces all very good at reflecting sound, sound field in room that is diffuse - (no shadows) but this is atypical of rooms.

Most rooms have 3 sound fields:

Near field - within 1 wavelength of lowest frequency of sound produced by source. Within this distance SPL measures vary widely. For human male voice, this = 11 feet.
Reverberant field - near large obstructions e.g. walls, reverberant (diffuse) sound predominates and SPL level relatively constant.
Free (far) field - field between near and reverberant field where inverse square law applies i.e. decreasing 6 db for doubling distance. Meaningful SPL measures can be taken.

Absorptive Materials (all types absorb sound by turning this into heat energy) - 3 types:

fibrous materials - absorb sound by frictional drag on air moving through pores. Absorption depends on thickness, density, porosity, and resistance to air flow. Air paths must extend from one side of material to other, therefore painting porous material ruins its absorptive capacity. High frequencies better absorbed than low frequencies. Absorption always proportional to thickness.
volume resonators - (Helmholtz resonators) air cavity within large enclosure. Designed to absorb narrow band of frequencies. Connected to surrounds by narrow neck. Impinging sound causes air at neck to vibrate, air mass vibrates and container absorbs this (e.g. shielding transformer hum at 120 Hz).
panel resonator - thin plywood or other material in front of a sealed airspace containing absorbent material. Alternating air pressure causes panel to deform and start moving and because material contains inherent stiffness to deformation, sound energy converted into heat by this internal damping.

Sound Transmission

Transmission loss (TL) is ratio of radiant acoustic energy over incident acoustic energy (in dB), therefore for two adjacent rooms, noise reduction (NR) is different in intensity between these. NR = ILroom 1 - ILroom 2

Average Transmission Loss - Sound Transmission Class (STC)

Transmission loss average across various frequencies (usually 16 x 1/3 octave bands). This approach takes flaws in barrier performance at certain frequencies into account. Recommended STC ratings are given for different types of environment e.g.-

Normal Quiet required for adjacent offices 38-40, for adjacent confidential rooms 45-50, for adjacent hotel bedrooms 50-52, for adjacent classrooms 40-42.

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