Acoustics 101

Acoustics: Definitions

Frequency and Wavelength

Frequency (f) is the time rate of a periodic signal. The unit is Hz (Hertz). Pure tone or sine wave has a single frequency. Sound and noise usually are not pure tones. Fourier Transform shows that the complex signal can be synthesized from sine signals (or pure tones) of different frequencies, different amplitudes and different time delays or (phases). Using this transform sound can be described as pure tones with defined amplitudes (or intensities). We can hear sounds with frequencies 16 Hz to 20,000 Hz. The human hearing system (the ears and related perception system in the brain) is more sensitive to frequencies around 1000 Hz to 4000 Hz.
The following drawing illustrates frequency ranges of few sounds:

The wave has frequency therefore it must has what is called wavelength, which is the distance the sound travels in one cycle time. The higher the frequency the shorter the wavelength.

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Sound Levels and Decibel

These terms are related to the amplitude of the signal. The absolute value of the sound intensity (I) can be described in Watts per square meter or W/m², and 10 log (relative intensities) is the sound level in dB. In sound application the reference value is 20 µPa for sound pressure or 10E-12 W/m² for sound intensity. The sound level of the reference values is 0 dB. This level represents the human threshold of hearing (the lowest level of sound that one can perceive). The threshold of pain or feeling (the level that causes pain in the ears) is about 120 dB. Decibel values cannot be added to obtain the value of the resulting sound. Instead the combined levels are turned into intensities, added together and then turned back into decibel values.

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Sound Absorption Coefficient

Sound absorption coefficient describes the efficiency of the material or the surface to absorb sound. The ratio between the absorbed sound energy and the incident energy is the sound absorption coefficient.

The most common way to measure sound absorption coefficient is to lay a piece of the material in the reverberant room (a room which has very long Reverberation Time) then measure RT so that the coefficient can be derived from Sabin equation (the original version of RT calculation). There is a standard that details this procedure. The value of the coefficient for the same material varies with the type of the mounting in the test room. Mounting types that are frequently given in manufacturer's data sheets of the acoustical panels are illustrated in the following drawing:

Noise reduction coefficient NRC is the arithmetic average, rounded off to the nearest multiple of 0.05, of the sound absorption coefficients at 250, 500, 1000, and 2000 Hz.

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Acoustical Simulation

Acoustical simulation is a technique that assists the acoustical consultants in the evaluation of the room acoustics or the performance of the sound systems. In addition to these studies, acoustical simulation can simulate the sound as it would be heard after the project is built. This simulation is called auralization.

The physical data of the room is entered into the acoustical program, or the AutoCAD file can be used to transfer the data. The data entry includes surface materials, background noise, and the seating layout.

Several acoustical simulation programs are in use, the popular programs are EASE and CATT.

Some of the acoustical factors that can be studied in such programs are: reverberation time, intelligibility, echo, sound levels over the seating areas, and many othrers. The animation shows ray tracing from a loudspeaker in a simple room.

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TEF Measurements

The Time-Energy-Frequency (TEF) measurements and analysis is a technology that uses a swept sinewave test signal. The TEF device is controlled by a personal computer. The available domains in TEF measurements include energy-frequency, energy-time, frequency-time, and energy-frequency-time.

An example of the energy-time domain is the reverberation time measurement as shown in the following figure:

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Sound Diffusion and Diffusers

Sound in an enclosure can be described as a diffused sound if the intensity of the sound energy is equal in any location of the room, or the sound energy flows equally in every direction. Many different factors can enhance the diffused sound. These include: geometrical irregularities, absent of focusing surfaces, absorptive and reflective elements randomly scattered throughout the space, and the existence of diffusing objects (furniture) or panels (diffusers).

Diffusing panels scatter sound in defined directions depending on their type and the geometrical dimensions.

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Reverberation Time (RT)

Reverberation time is the time required for the sound level in the room to decay 60 dB, or in other words, it is the time needed for a loud sound to be inaudible after turning off the sound source. This concept is shown in the following drawing:

The calculation of reverberation time using the Sabin equation assumes that the sound in the room be diffused. In practice, RT equations are good enough to describe the sound build up and attenuation in the room. In the case where the sound in the room is not diffused enough, such as rooms with good absorption surfaces in certain areas, or with an unusual shape (long and narrow, very low ceiling, or has many different focusing surfaces), the RT calculation is not accurate. There is Fitzroy equation to correct the RT calculation for rooms with good absorptive surfaces on certain axes of the room.

The optimum reverberation time for different rooms depends on the volume of the space, the type of the room, and the frequency of the sound. In general terms, the optimum RT for rooms with speech programs is less then the optimum RT for rooms with music performance.

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Noise Paths

Noise paths in a building are illustrated in the following figure:

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Noise Levels

The human hearing system has different sensitivities at different frequencies. This means that the perception of noise is not equal at all frequencies. Noise with significant measured levels (in dB) at high or low frequencies will not be as annoying as it would be when its energy is mainly in the middle frequencies. In other words, the measured noise levels in dB will not reflect the actual human perception about the loudness of a noise. A specific circuit is added to the sound level meter to correct its reading. This reading is the noise level in dBA. The letter A is added to indicate the correction that was made in the measurement.

The following table displays A-weighted sound levels for some common noises:

Small office	Large office	Car 65 mph at 25'	Light traffic at 100'	Quiet residential (daytime)	Quiet residential (nighttime)	Sewing machines at 3'
50-55 dBA	60-65 dBA	70-80 dBA	50-60 dBA	40-50 dBA	30-50 dBA	95-100 dBA

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TL, STC and IIC

The transmission loss (TL) for a partition is defined as the difference in decibels between the sound intensities on two sides of the barrier.

Sound transmission class (STC) is a single number used to characterize the air-borne isolation properties of a partition. The STC is determined from the TL measured at different frequencies. These measured values are then compared with a family of STC reference contours. Simple rules apply in choosing the appropriate contour. For example: STC for painted concrete block depends on its weight, but will be in the range of 45-48 for 8", and of 47-51 for 12".

The STC of the composite structure (wall and window for example) is not the sum of the STC of its components. We have first to calculate the TL for the composite wall (taking into account the surface area of the components) then find the STC rating.

Impact isolation class (IIC), like STC, is another single-number rating system for a solid-borne noise (floor-ceiling structure). The higher the IIC rating, the more efficient the construction will be in attenuating the impact sound within the frequency range of the IIC. For example: 6" reinforced concrete slab (75 lb/sq ft) has IIC 34, and more then 54 when carpet with pad cover the floor.