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Bucur [2006] provided a thorough reference text on the use of acoustics for non- destructive testing of wood. She noted that measurements of acoustic dispersion and attenuation in wood are complicated by various factors. These include the physical properties of the substrate, i.e., the wood’s elastic and viscous properties; the geometrical characteristics of the specimen under test, both macro-structural and micro-structural; the environmental conditions including temperature, moisture content, and mechanical loading; and the measurement conditions including the sensitivity and frequency response of the transducers, their size and location, the coupling medium, and the dynamic characteristics of the electronic equipment. Bucur and Feeney [1992] noted that the two principle causes of attenuation in wood arescattering and absorption. Scattering, they noted, is usually related to the size of the wavelength relative to the size of the wood fibres. They also explained that ultrasonic velocity and attenuation are best studied by choosing a source frequency such that the acoustic wavelength lies roughly in a range between the maximum dimension of the anatomical elements and the minimum specimen dimension.

The amount of attenuation in wood is typically expressed in units of dB/cm. The spatial gain of an acoustic wave can be expressed in decibels,

AdB= 20 log10 exp (−zα)

(4.2)

=−8.686zα (4.3)

where exp is the exponential function, and α is the attenuation coefficient, which is equal to−Im{k}, wherek is the wavenumber (see (2.36)), and has units of m−1. The attenuation3 in dB/cm is then given by

αdB/cm=− 8.686

100 α. (4.4)

Bucur [2006] stated that the attenuation coefficient for compressional waves travelling along the grain is on the order of 2 dB/cm.

A common method of measuring acoustic attenuation in wood is via a pulse transmission technique [Bucur and Feeney 1992]. In this method, a transducer is attached to either side of a small wood sample. One of the transducers is driven using a pulse generator. The generator typically drives several cycles at an ultrasonic frequency (potentially ranging from about 100 kHz to several MHz). The attenuation coefficient is deduced by taking the ratio of the received-signal amplitude through the sample to the amplitude with no wood sample between the transducers. Either compressional or shear mode transducers can be used. The transducers can be placed across any of the sample’s faces, depending on whether the operator wants to measure along the L, R, or

3

αdB/cmis also referred to as theattenuation coefficient, or theabsorption coefficient, though it is

T directions.

Okyere and Cousin [1980] used the pulse transmission technique to find the attenua- tion of longitudinal stress waves in small samples of four different species: White spruce, Red pine, American beech, and Red oak. Ultrasonic pulses were generated at frequencies of 250 kHz, 500 kHz, and 1.0 MHz. They found that each of the measured species displayed a trend of increasing attenuation with frequency. The range of the attenuation coefficients was between 0.5 dB/cm (Red oak at 250 kHz) to 5.0 dB/cm (White spruce at 1.0 MHz). Kamioka [1988] used pulse transmission to evaluate the longitudinal attenuation coefficient of Red lauan wood. Specifically, the effect on the response due to various different coupling substances was examined. Grease was determined to be the ideal coupling material, producing the largest response amplitude. The longitudinal attenuation coefficient of the wood sample due to an ultrasonic pulse of 1 MHz was found to be 1.62 dB/cm. Bucur and Feeney [1992] used pulse transmission to determine the ToF velocity and the acoustic attenuation of small samples ofAesculus hypocastanum

(horse chestnut). The transducer was pulsed at ultrasonic frequencies ranging from 100 kHz to 1.5 MHz. This was conducted in each of the principle directions; L, R, and T; for both longitudinal and shear modes. They observed significant dispersion in the longitudinal direction between 100 kHz and 250 kHz, with the velocity increasing from approximately 3000 ms−1 to 4000 ms−1. The attenuation over this range was not quoted.

Another method of determining acoustic attenuation is by measuring the decay of reverberations within a sample. It was noted by Dunlop [1983] that the rate of decay is inversely proportional to the amount of absorption in the medium. Ouis [2000] used this technique to find the decay of an induced wave in a harvested log. He measured the decay due to an impulse-like signal in a log of Picea Abies, but did not provide a figure for the attenuation coefficient. This method requires that a fixed, known length wood-sample is used. It is therefore unsuitable for use on standing trees, where the ToF method is typically employed.

Studies performed using the pulse-transmission technique have noted that both acoustic velocity and attenuation tend to increase as the pulse frequency is increased [Bucur and Feeney 1992, Okyere and Cousin 1980]. Ouis [2002] provided a theoretical basis for this finding. He explained that the effective stiffness of wood (and most other solids) is expected to increase with frequency. Ouis explained that this follows from the fact that an acoustic medium is causal, i.e., no output response can precede its input. A consequence of this causality is that the real and imaginary parts of the frequency response are interrelated. Ouis [2000] explored a dispersive model of a viscoelastic medium, known as the fractional Zener model (defined by [Pritz 1996]) which could potentially be applied to wood studies. Ouis did not apply the viscoelastic model to experimental data, he only hypothesised on the form of the dispersion model for wood.