# D : Sound and Vibration Terms, Definitions, Units, Measurements ...

**Daily Exposure - vibration : Aeq8** : the vibration a worker is exposed to during a working day, normalized to an 8-hour reference period, taking account of the magnitude and duration of the vibration - more details.

**Daily Exposure Level : LEX,8h** : is the
Sound Exposure **averaged** over 8 hours.

The Noise at Work Directive 2003/10/EC : defines the following limit and action values:

**Exposure Limit Values: LEX,8h** = 87 dB(A) and LCpeak = 200 Pa respectively;

**Upper Exposure Action Values: LEX,8h** = 85 dB(A) and LCpeak = 140 Pa respectively;

**Lower Exposure Action Values: LEX,8h** = 80 dB(A) and LCpeak = 112 Pa respectively.

### LCpeak is the maximum value of the
C-weighted, instantaneous noise pressure.

**see also** : Daily Personal Noise Exposure LEP,d

**LEX,8h** : is the Leq - Equivalent Continuous Sound Level corrected for the length of the working shift, in this case 8 hours

**Daily Personal Noise Exposure : LEP,d**: is the average
A-weighted noise exposure level for a nominal 8-hour working day, also known as LEX,8h. Used for assessing the noise exposure of a worker during a working day.

**LEP,d** is calculated from the measured Sound Exposure the Exposure Time and a Reference Time of 8 h.

### If the Leq is measured over 8 hours then Leq and LEP,d and LEX,8h would all be the same.

#### The European Directive recommends LEX,8h is adopted from 2006 onward.

**Damping** : any means of dissipating vibration energy within a vibrating system.

## The dissipation of energy with time or distance. The term is generally applied to the attenuation of sound in a structure owing to the internal sound-dissipating properties of the structure or to the addition of sound-dissipative materials.

### The action of frictional or dissipative forces on a dynamic system causing the system to lose energy and reduce the amplitude of movement.

#### Removal of echoes and reverberation by the use of sound absorbing material.

**Damping Ratio** : ratio of the actual damping to the Critical Damping.

**DAT Recorder** : Digital audio tape recorder.

**Data Logging** : on-going measurements, stored at regular intervals for downloading to a PC.

**Data Source** : the identity and location of the data that are used in an analysis.

**dBA, dBB, dBC, dBD, dB Flat, dB Linear and dBZ** : Frequency Weighting filters.

# dB Level : is the Logarithm of the ratio of a given acoustic quantity to a reference quantity of the same kind. The base of the logarithm, the reference quantity, and the kind of level must be indicated.

**Note 1** : the kind of level is indicated by use of a compound term such as Sound Power Level or Sound Pressure Level.

**Note 2** : the value of the reference quantity remains unchanged, whether the chosen quantity is Peak, the RMS, or otherwise.

**Note 3** : the base of the logarithm is indicated by use of a unit of level associated with that base.

**dBm : dB(mW)** : power relative to 1
Milliwatt. No reference impedance is assumed, though 600 ohms is common in audio equipment.

**dBu** : dB (0.775 V rms) : voltage ratio with a reference voltage of Vo = 0.7750 volt = 0 dBu, derived from a 600 ohms load dissipating 0 dBm (1 mW)

**dBV** : dB (1 Vrms) : voltage ratio with a reference voltage of Vo = 1.00 volt = 0 dBV, regardless of impedance.

L in dB = 20 · lg (V/Vo)

**dBW** : or decibel watt is a unit for the measurement of the strength of a signal expressed in decibels relative to one watt. It is used because of its capability to express both very large and very small values of power in a short range of number, e.g. 1 watt = 0 dBW, 10 watts = 10 dBW, 100 watts = 20 dBW and 1,000,000 W = 60 dBW.

## Power in dBW = 10 lg (Power in W)

**DC Coupling** : the connection of a signal from one circuit to another in a manner that passes both AC and DC components

**Decay Rate : d** : is the time taken for the
Sound Pressure Level in a room to decay - measured in
decibels per second (dB/s).

## Decay rate d in a reverberant room is related to the
Reverberation Time T by the formulae T = 60 dB / d.

**Decay Time** : the time taken for the Sound Pressure Level to fall by 60 dB - a million to one.

**decibel : dB** : a relative unit of measurement widely used in acoustics, electronics and communications. The dB is a
Logarithmic unit used to describe a ratio between the measured level and a reference or threshold level of 0dB. The ratio may be
Sound Power,
Sound Pressure, voltage or
Sound Intensity, etc.

**decibel scale** : a linear numbering scale used to define a
Logarithmic amplitude scale, thereby compressing a wide range of amplitude values to a small set of numbers.

| **Vibration Levels** | **Sound Levels** |

| Acceleration : La | Velocity : Lv | Particle Velocity : Lv | Pressure : Lp |

dB | m/s^{2} | m/s | m/s | Pa : N/m^{2} |

0 dB | 1 x 10^{-5} | 1 x 10^{-9} | 5 x 10^{-8} | 2 x 10^{-5} |

20 dB | 1 x 10^{-4} | 1 x 10^{-8} | 5 x 10^{-7} | 2 x 10^{-4} |

40 dB | 1 x 10^{-3} | 1 x 10^{-7} | 5 x 10^{-6} | 2 x 10^{-3} |

60 dB | 1 x 10^{-2} | 1 x 10^{-6} | 5 x 10^{-5} | 2 x 10^{-2} |

80 dB | 0.1 | 1 x 10^{-5} | 5 x 10^{-4} | 0.2 |

100 dB | 1.0 | 1 x 10^{-4} | 5 x 10^{-3} | 2.0 |

**Table Notes :**

0 dB is the reference level for each parameter.

The parameters above use the 20 Lg formulae for example : 20 Log10 (P/Po) dB for Sound Pressure Levels.

The parameters below use the 10 Lg formulae for example : 10 Log

10 (I/Io) dB for

Sound Intensity Levels.

**Degree** : ° : a measure of angles. There are 360 degrees in a full rotation or circle and 90 degrees (90°) is a right angle. The symbol for degree is °

**Delay** : a time difference that has to elapse after (or before) triggering of a measurement and sampling of the time history data begins. There are situations where entering a trigger delay is useful.

**Density : ρ** : the density of a material is it's
Mass per unit
Volume.

## ρ = m/V where ρ is the density, m is the mass and V is the volume.

### SI units: kilogram per cubic metre, kg/m^{3}

**Density of air** :
Air density decreases with increasing altitude, as does air pressure.

At sea level and at 20 °C, air has a density of approximately 1.2 kg/m^{3}

At sea level and at 0 °C, air has a density of approximately 1.3 kg/m^{3}

**Detector** : an electronic circuit that determines the amplitude level of a signal in accordance with certain rules. The simplest type of detector consists of a resistor and a capacitor, which measures the rectified average value of a fluctuating DC signal. A more complex and much more useful type of detector is an RMS detector whose output is proportional to the
Energy in the Waveform.

**Deterministic** : a type of signal whose spectrum consists of a collection of discrete components, as opposed to a random signal, whose spectrum is spread out or smeared in frequency. Some deterministic signals are periodic, and their spectra consist of harmonic series. Vibration signatures of machines are in general deterministic, containing one or more harmonic series, but they always have non-deterministic components, such as background noise.

**Differentiation : ** in acoustics, a mathematical operation that converts a Displacement signal to a Velocity signal, or a velocity signature to an Acceleration signature. The opposite process is called Integration

**Digital Filter** : a digital processor that receives a sequence of input data values, executes an operation on them, and outputs a corresponding sequence of values that have been filtered with respect to the input.

**Digital Filter Analyser** : constant percentage (or relative) bandwidth resolution. This is often preferred for acoustic measurements because it best simulates the way in which the human ear perceives sound.

**Digital Signal Processing : DSP** : is the analysis of digital signal data. The original analogue signal is sampled at regular time intervals, and an Analogue to Digital converter converts the sampled amplitudes into a number series.

**DIRAC : Dual Input Room Acoustics Calculator** : software developed by Acoustic Engineering to measure a wide range of room acoustical parameters, according to the ISO 3382 (room acoustics) and IEC 60268-16 (speech intelligibility) standards. Based on the measurement and analysis of impulse responses, DIRAC supports a variety of measurement configurations and is distributed by Bruel & Kjaer.

**Direct Sound** : the region in which the sound measured can be attributed to the source alone without the effects of obstructions, walls, other reflecting surfaces or adjacent noise sources.

**Directivity Factor : Q** : by definition a noise source that radiates uniformly in all directions, spherically has a Q = 1.

## Place the same source on the ground so the energy can only radiate hemi-spherically, then the Directivity Factor Q=2.

Place the source on the ground next to a wall so the radiation is concentrated into a 1/4 of the sphere, then Q=4.

If the source is placed on the floor in a corner, the sound energy is further concentrated into 1/8th of a sphere so Q = 8.

**Directivity Index : DI** : is 10 times the logarithm to the base 10 of the Directivity Factor Q.

## Say for example we buy a piece of equipment with a sound power rating of 80 dB and we install it in the corner of an empty building. The resultant sound power level radiated into the building would be 80 dB + 10.log(8) = 89 dB.

**Directivity Pattern** : a graphical description, usually in polar co-ordinates, of the response of the transducer as a function of the direction of the transmitted or incident sound waves in a specified plane and at a specified frequency.

**Discrete** : with reference to a spectrum, discrete means consisting of separate distinct points, rather than continuous.

**Discrete Fourier Transform : DFT** : mathematical calculation that converts or transforms a sampled and digitised waveform into a sampled spectrum. They reveal periodicities in input data as well as the relative strengths of any periodic components. The Fast Fourier Transform : FFT, is an algorithm that allows a computer to calculate the discrete Fourier transform very quickly.

**Dispersion** : separation of the sinusoidal components of a wave that results from change of speed of sound with frequency.

**Displacement : s** : change in position of an object in metres - vector quantity.

## v = u + at where v = velocity, u = start velocity, a = acceleration in m/s^{2} and t = time.

#### Velocity v = a/ω

Displacement s = v/ω

It follows that 10 m/s^{2} = 0.01 m/s = 10 μm at 159 Hz

This works for all frequencies, we just chose 159 Hz to keep the numbers simple. We also have a Vibration Nomogram for downloading.

**Distance** : change in position of an object in metres -

**see also** : Displacement above.

**Distortion** : signal components not in the original signal due to non linearities in the system or transmission path.

**Divergence Loss** : that part of the transmission loss due to the divergence, i.e. spreading, of sound waves in accordance with the configuration of the system, also known as Spreading Loss.

**Note** : Divergence Loss exists, for example, for spherical waves emitted by a point source.

**DOD** : Department of Defence : USA.

**Dodecahedron** : A general dodecahedron is a polyhedron having 12 faces. Acoustic examples are dodecahedron and hemi-dodecahedron loudspeakers arrange to provide Isotropic sound sources.

**Dual Input Room Acoustics Calculator** : DIRAC

**Dynamic Range** : all audio systems are limited by inherent noise at low levels and by overload distortion at high levels. The usable region between these two extremes is the dynamic range of the system. Expressed in dB.

**Dyne** : the force that will accelerate a 1 gram mass at the rate of 1 cm/s. The old standard reference level for Sound Pressure was 0.0002 dyne/cm². The same level today is expressed as 20 micro Pascals, or 20 μPa

1 dyne = 1 g·cm/s^{2} = 10^{-5} kg·m/s^{2} = 10 μN