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

**1/n-octave** : analysis made on a fractional part of an Octave where n is the variable. Commonly used values are 1/1, 1/3, 1/12 and 1/24-octave.

**A/D Converter** : converts a Analogue signal to a Digital signal.

**AC Coupling** : the connection of a signal from one circuit to another in a manner that rejects DC components.

**Accelerance** : complex ratio of acceleration to applied force.

**Acceleration : a** : is the rate of change of
Velocity and is a
Vector quantity.

## The SI units are m/s^{2} or if using Imperial units then 'g' = 9.80665 m/s^{2} = 386.089 in/s^{2}

#### Velocity = a/ω

Displacement = v/ω

So at 159 Hz an acceleration of 10 m/s^{2} = 0.01 m/s and = 10 μm

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

If 1 N = 1 Kg·m/s^{2}, it follows that m/s^{2} acceleration also equals N/kg Newtons per kilogram.

**Amax** : is the maximum RMS Acceleration.

**Amax** : is the maximum RMS Acceleration.

**Amp** : is the maximum Peak Acceleration.

**aw** : is time-averaged, frequency-weighted, single-axis vibration acceleration.

**The human response to vibration covers a wide range from a few
μm/s**^{2} to tens of metres per second squared. The dB scale is a useful way to represent the immense range using a manageable set of numbers.

**Acceleration Level dB : La** = 20 lg (a/ao) dB re 1 µm/s^{2} - also known as **Vibration Acceleration Level**

an increase or decrease in acceleration of 20 dB = a factor of 10

a 40 dB = a factor of 100

a 60 dB = a factor of 1000 ... etc.

**Acceleration Reference Level : ao = 10**^{-6} m/s^{2} (defined in ISO 1683) *

**Acceleration Equivalent Level : Aeq** : a single number to represent the equivalent acceleration energy as it varies over a working day, measured in m/s^{2}

## For example Aeq8 = 2.5 m/s^{2} indicates a equivalent level of 2.5 m/s^{2} measured over an 8 hour shift.

### To calculate the equivalent value for other periods use the formulae Aeq8 = a √T/8 where T = hours

Aeq4 and Aeq16 are also used in some vibration exposure applications.

**Accelerometer** : a sensor whose electrical output is proportional to acceleration, intended for measurement of vibration. The two most common types are the traditional Charge type and the IEPE, Integrated Electronic PiezoElectric type with a built-in line-drive amplifier to enable the output signal to be transmitted over 'longer cable runs'.

**ACGIH** : American Conference of Industrial Hygienists.

**Acoustic Calibrator** : an instrument providing a reference noise source used to calibrate and check the performance of sound level meters.

**Acoustic Coupler** : cavity of predetermined shape and volume used, for example, for the calibration of earphones or microphones in conjunction with a calibrated microphone adapted to measure the sound pressure developed within the cavity.

**Acoustic Emission** : the energy that is generated when materials are under stress or break.

**Acoustic Impedance ** : is the opposition to the flow of sound through a medium.

**Acoustic Impedance : Z, Za** : at a surface is the complex ratio of the effective Sound Pressure averaged over the surface to the effective Volume Velocity through it.

### Za = p/Q : the SI Units are Pa·s/m^{5} (MKS units: acoustic ohms)

**Characteristic Acoustic Impedance : Zo ρc** : is the ratio of the effective Sound Pressure at a given point to the effective Particle Velocity at that point. In a Free Progressive Wave, it is equal to the product of the Density ρ of the medium times the Speed of Sound c in the media.

### Zo = ρc : the SI units are N·s/m^{3}.

For example at room temperature and normal atmospheric pressure, ρc = 415 N·s/m

^{3}

**Complex Acoustic Impedance** : in general, a phase relation exists between the pressure and the particle velocity and the complex impedance is defined as Z = R +iX

### where R is the resistive part, and X is the reactive part of the impedance The resistive part represents the various loss mechanisms an acoustic wave experiences such as random thermal motion.

For the case of propagation through a duct, wall vibrations and viscous forces at the air/wall interface (boundary layer) can also have a significant effect, especially at high frequencies for the latter. For resistive effects, energy is removed from the wave and converted into other forms. This energy is said to be 'lost from the system'.

**Specific Acoustic Impedance : z** is the ratio of the effective Sound Pressure at a point in an acoustic medium to the effective Particle Velocity at that point.

### z = p/v : the SI units are Pa·s/m^{3} or rayls in MKS units.

The real part of the acoustic impedance is termed **Acoustic Resistance**.

The imaginary part is termed **Acoustic Reactance**.

**Acoustic Louvre** : a specially built louvre designed with sound-attenuating baffles for reduction of airborne sound.

**Acoustic Ohm** : is a unit of measurement of sound resistance, and is the ratio of the Sound Pressure to Volume Flow m^{3}/s = Pa s/m^{3}.

## These units got their name by analogy with electric resistance, which is measured in ohms.

**see :** Acoustic Impedance above.

**Acoustic Phase Coefficient** : imaginary part of the linear exponent of sound propagation.

**Acoustic Power** : also known as Sound Power is the Sound Energy measured over a stated period of time.

**Acoustic Pressure : p ** : more commonly known as
Sound Pressure is the difference between the pressure produced by an acoustic wave and the Atmospheric Pressure at a given point in space, and is measured in Pascal - symbol Pa, units Newton per square metre.

## 1 Pa = 1 N/m^{2} = 1 J/m^{3} = 10^{-5} bar = 1 kg/(m·s^{2})

**more details under** Sound Pressure

**Acoustic Radiation Pressure** : unidirectional steady pressure exerted on a surface by an acoustic wave.

**Acoustic Reactance** : the imaginary part of Acoustic Impedance

**Acoustic Resistance** : the real part of Acoustic Impedance

**Acoustic Trauma** : damage to the hearing mechanism caused by a sudden burst of intense noise, or by a blast. The term usually implies a single traumatic event.

**Acoustic Velocity** : under Speed of Sound - not to be confused with.

**Active Noise Control** : reducing unwanted sound electronically. When a sound wave of equal amplitude but opposite sign (180 degree out of phase) is added to the original sound the result is sound cancellation.

**Airborne Sound** : sound that reaches the point of interest by propagation through air.

**Air Condenser Microphones** : are widely used in noise measurements because they offer the best linearity, frequency range and high stability.

## Because of their importance we have prepared more details Measurement Microphones

**Algorithm** : a specific procedure for solving mathematical problems. An FFT is an algorithm.

**Aliasing** : digital sampling requires the analogue signal to be sampled at twice the frequency of interest otherwise aliasing occurs. If the signal is not filtered to eliminate the high frequencies, they appear as 'false' lower frequency signals. Once 'introduced' these aliased signals cannot be distinguished from valid sampled data.

**Ambient Noise** : the total noise, at a given place, a composite of sounds from many sources near and far.

**Ambient Pressure** : the ambient pressure is the pressure of the surrounding medium. The SI unit is the Pascal - Pa which is very small relative to the Atmospheric Pressure.

**Ampere : A** : the basic SI unit of electric current; the constant current that, when maintained in two parallel conductors of infinite length and negligible cross section placed 1 metre apart in free space, produces a Force of 2 x 10^{-7} Newton per metre between them.

1 ampere is equivalent to 1

Coulomb per second

**Amplification Factor : Q** : the mechanical gain of a structure when excited at a Resonant Frequency.
The amplification factor is a function of the system Damping.

## For a Damping Ratio = 0 (no damping) the amplification factor is infinite, for = 1 (critically damped) there is no amplification.

**Amplitude** : the magnitude of an oscillating quantity, for example
Sound Pressure or Vibration Level. In the case of a vibrating object, the amplitude is measured and expressed in three ways: Displacement, Velocity and Acceleration. Amplitude is also the y-axis of the vibration time waveform and spectrum; it helps define the severity of the vibration.

**Amplitude Distribution** : a representation of time-varying noise indicating the percentage of time that the noise level is present in a series of amplitude intervals.

**Amplitude Probability** : used to investigate the amplitude distribution of signals. Also 'known' as probability amplitude.

**Analogue** : continuously variable physical quantity, such as a sound or vibration wave.

**Analogue to Digital Converter** : converts an Analogue signal to a Digital one. US spelling analog.

**Anechoic** : without echo - refers to the absence of sound reflections. It is almost impossible to create a truly anechoic environment, as there is no such thing as a perfect Sound Absorber, an expensive Anechoic Chamber is as close as it gets. Measurements in a field well away from reflective surfaces and any other sound sources can approximate to semi-anechoic conditions.

**Anechoic Chamber** : echo free room, within specified limits Walls lined with Sound Absorbent wedges to minimize reflections and create Free-field conditions, so direct sound measurements of test objects may be made. Low frequency measurements are restricted by the room dimensions and the sound absorbing materials 'wedges' used.

**Angles**: angles are usually expressed in degrees or radians. Less often as Grads or Gradians (except on some electronic calculators)

Units | Values |

Degrees | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |

Radians | 0 | π/6 | π4 | π/3 | π/2 | π | 3 π/2 | 2π |

Grads | 0^{g } | 100^{g}/3 | 50^{g} | 200^{g}/3 | 100^{g} | 200^{g} | 300^{g} | 400^{g} |

**Angular : **Physical properties or quantities measured with reference to an angle, especially those associated with rotation

### Units : Radians per second squared, rads/s^{2}

## This is because it provides a very simple relationship between distance travelled around the circle and the distance r from the centre.

### θ = s/r = length of arc divided by the radius in
Radians

**Angular Frequency : ω** : the frequency expressed in Radians per second (rad/s).

## To convert a Frequency in hertz to an angular frequency multiply by 2·π

For an oscillation with Period T, the angular frequency ω = 2·π / T

**Angular Momentum : L ** : the quantity of rotation of a body, which is the product of the
Moment of Inertia and it's angular velocity :

## Units : newton metre seconds (N·m·s)

**Angular Velocity : v** : the rate of change of angular position of a rotating body

## Units : radians per second, rads/s

**ANSI : American National Standards Institution. **:

**Anti-aliasing Filter **: analogue low pass filters used before analogue to digital conversion to filter out the frequencies greater than half the sampling frequency and prevent Aliasing

**Antinode** : the point of maximum displacement in a periodic system.

**Note** : the appropriate modifier should be used to signify the other types; e.g. Particle Velocity Antinode or Sound Pressure Antinode

**Apodization Function** : also called a tapering or Window Function. It provides a smooth amplitude weighting of a signal to zero at the beginning and the end of the record to be sampled. This suppresses Leakage which would otherwise be produced upon performing a Discrete Fourier Transform.

**Area : A** : a quantity expressing the two-dimensional size of a defined part of a surface.

**Surface Area** refers to the total area of the exposed surface of a 3-dimensional solid.

## The derived SI unit is the square metre, symbol : m^{2} : 1 m^{2} = 1 m by 1 m or 2 m by 0.5 m, etc.

25 mm by 25 mm = 0.025 m by 0.025 m = 0.000625 m^{2}

**Artificial Ear** : device for the calibration of earphones, incorporating a calibrated microphone for the measurement of Sound Pressure and an Acoustic Coupler such that the overall Acoustic Impedance is similar to that of the normal human ear in a given frequency band.

**Artificial Mastoid** : device which simulates the mechanical impedance of the average human mastoid where a bone vibrator may be applied to permit calibration of the vibrator.

**Artificial Mouth** : device consisting of a loudspeaker unit mounted in a baffle or an enclosure so shaped as to have a radiation pattern similar to that of the average human mouth.

**Artificial Reverberation** : Reverberation generated by electrical or acoustical means to simulate that of concert halls, etc., Added to a signal to make it sound more lifelike.

**Artificial Voice** : a complex sound, usually emitted by an **Artificial Mouth**, whose spectrum corresponds to that of the average human voice.

**ASHRAE** : American Society of Heating, Refrigeration and Air-Conditioning Engineers.

**Asymmetric** : a waveform not identical on both sides of the mean or zero line, lacks symmetry.

**Atmospheric Absorption** : up to a few hundred metres atmospheric absorption can be ignored. At greater differences it can be significant particularly at frequencies above 1 kHz.

**Atmospheric Pressure : atm** : is the Force per unit area exerted on a surface by the weight of air above that surface.

**Standard Atmospheric Pressure**, at sea level, is equal to 101.325 kPa the preferred SI units or 8760 mmHg and 1013.25 Millibars.

**Attenuation Coefficient** : real part of the linear exponent of sound propagation.

**Note** : the unit is the Neper per metre.

**Audible Range** : the human ear can respond to minute
Pressure variations in the air if they are in the
Frequency range, roughly 20 Hz - 20 kHz and Wavelength 17 m to 0.017 mm.

**Audiogram** : graph showing hearing loss as a function of frequency, measured with an audiometer.

**Audiometer** : an instrument for testing hearing, standard equipment in ENT, Audiometry and Audiology Centres.

**Auditory Masking** : occurs when the perception of one sound is affected by the presence of another sound.

**Autocorrelation** : the Correlation between values of a signal at different times. A signal processing tool for finding repeating patterns, such as the presence of a Periodic signal(s) 'buried in noise'. It is frequently used for analysing Time Domain functions. It is the Cross-correlation of a signal with itself.

**Auto Scale**: the axes of the graph used to display time signal, spectra, post-processed functions, etc., are automatically set by the software to fit the full display into the available viewing area.

**Autospectrum** : for FFT measurements, the Fourier Transform of a time signal is complex as it has magnitude and phase. The autospectrum is the average of the squared magnitude. For 1/n-octave Constant Percentage Bandwidth measurements, it is the mean square of the filter output.

**Average** : in acoustics where dB levels are extensively used, average may not mean adding up the values and then dividing by the number of samples. See our discussion Calculations using the decibel and the other **Averaging** entries below.

**Averaging : various methods of 'signal processing' are used in acoustics**

**aw** : is the time-averaged frequency-weighted, single-axis vibration acceleration.

**Axial Mode **: the room resonances associated with each pair of parallel walls in a rectangular room.