Hearing Equations

where:
Lp1= Sound pressure level in decibels at location 1.
Lp2= Sound pressure level in decibels at location 2
R1 = Distance from noise source to point 1
R2 = Distance from noise source to point 2
(R1 and R2 must have the same units.)
 
Reverberation Time -- Time required for average sound pressure level in a room to decrease 60 dB after a steady state source stops generating sound. Can be estimated from:

Audible Frequency Range -- The range of sound frequencies normally heard by the human ear. The audible range spans from 20 Hz to 20,000 Hz, but for most engineering investigations only frequencies between about 40 Hz and 11,000 Hz are considered.

Background Noise -- The sound pressure levels in a given environment from all sources excluding a specific sound source being investigated or measured.

Broad Band Noise -- Spectrum consisting of a large number of frequency components, none of which is individually dominant.

Decibels -- Ten times the logarithm (to the base 10) of the ratio of two mean square values of sound pressure, voltage, or current. The abbreviation for "decibels" is dB.

Decibel Addition--

or, where L1 and L2 are Levels to be added, use the expression:

Example
80 dB + 74 dB = 81 dB

Frequency -- The number of cyclical variations per unit time. Frequency is generally expressed in cycles per second (cps) also denoted Hertz (Hz).

Noise -- Unwanted sound which may be hazardous to health, interferes with communications or is disturbing.

Octave Bands -- Frequency ranges in which the upper limit of each band is twice the lower limit. Octave bands are identified by their geometric mean frequency, or center frequency.

One Third Octave Bands -- Frequency ranges where each octave is divided into one-third octaves with the upper frequency limit being 2 1/3 (1.26) times the lower frequency. Identified by the geometric mean frequency of each band.

Preferred Frequencies -- Octave and one third octave band center frequencies are the geometric means of their respective lower and upper limits as defined by ISO and ANSI standards.

The upper and lower nominal octave band limits are arrived at by multiplying the center frequency by 1.4142 and 0.7071 respectively.

One-third octave band center frequencies are given by 10 (n/10) where n is the one third octave band number. For instance, for 125 Hz the band number is 21 and 10 2.1 = 125.89. Lower and upper frequency limits are a function of 2-1/6 or (0.89) and 2 +1/6 or (1.12) respectively.

Pink Noise -- Sound with an uninterrupted frequency spectrum and a power which is steady within frequency band and proportional to center frequency. An example is constant power level per octave band.

Pure Tone -- A sound emitted at a single frequency.

Sound Receiver -- One or more observation points at which sound is evaluated or measured. The effect of sound on an individual receiver is usually evaluated by measurements near the ear or close to the body.

Sound -- Sound is a vibrational disturbance, exciting hearing mechanisms, transmitted in a predictable manner determined by the medium through which it propagates. To be audible the disturbance must fall within the frequency range of 20 Hz to 20,000 Hz.

Sound Power -- The acoustic power of a sound source, expressed in Watts.

Sound Power Level (Lw)-- The acoustic power radiated from a given sound source as related to a reference power level (typically 10 -12 watts) and expressed in decibels as:

Sound Pressure Level (Lp)-- The ratio, expressed in decibels, of mean-square sound pressure to a reference mean-square pressure which by convention has been selected to be equal to the assumed threshold of hearing.

where:
Lp = Sound pressure level.
p = Root Mean Square sound pressure.
Reference pressure, pref = 2 X 10 -5 (N / meter 2) = 0.0002 dynes / cm2
= 0.0002 microbars
= 20 micropascals (RMS).
 
Sound Source -- Equipment or phenomena that generate sound. Source room: room containing sound source.

Spectrum -- A quantity expressed as a function of frequency, such as sound pressure versus frequency.

Speed of Sound in Air --
C = 49.03 (460 + T)1/2 in feet per second
where:
Cm = 20.05 (273 + Tc)1/2 in meters per second
C = Speed of sound in feet per second
T = Temperature in degrees Fahrenheit
Cm = Speed of sound in meters per second
Tc = Temperature in degrees Celsius

Speed of Sound in Engineering Materials
Structureborne Noise -- Generation and propagation of time-dependent motions and forces in solid materials which result in unwanted radiated sound.

Summation of Identical Sound Sources -- The total sound level generated by N identical sound sources is:
Lp(total) = Lp(single source) + 10 log N

where:
N = Number of sources

Summation of Unequal Sound Sources -- The total sound level generated by N sound sources Lp1, Lp2....LpN

Threshold of Hearing -- The lowest continuous sound pressure levels which will create an auditory sensation for the average human ear. Any sound below these levels will be inaudible and any sound above the threshold will vary in loudness dependent on intensity.

Transient Sounds -- Sounds which are audible for a limited period of time e.g.. sounds from airplane flyover.

Vibration Isolation -- Reduction of force or displacement transmitted by a vibratory source. Often attained by use of a resilient mount.

Wavelength -- The length in space of one complete cycle of a sound wave.

where:

White Noise -- A noise whose spectrum (level) density is substantially independent of frequency over a specified range and has equal power for any range of frequencies of constant bandwidth.