Resonant inspection of precious metals
For measurements of certain properties of thin materials, such as the thickness or birefringence – having different velocities of sound depending on the polarisation of the sound waves – of sheets or plates, resonant mode excitation can be used. This is often used in cases where the sample is too thin for conventional pulse-echo measurements as the echoes arrive so close together that they overlap in the time domain (the signals from multiple reflections arrive overlapping with each other, so you can’t tell the echoes apart), making direct time domain measurements impossible.
In this case the natural resonant frequencies of the various wavemodes can tell us information about the wave velocity or thickness of the sheet. These can be measured either by sweeping the frequency of the generation transducer until the maximum intensity of ultrasound is observed, or more simply be generating a broadband pulse of ultrasound (a pulse containing a wide range of frequencies, often consisting of a sharp “spike” or square pulse when observed in the time domain) and observing the frequencies that the sample resonates at.
This technique requires a Fourier transform to be performed on the time domain signal in order to reveal the resonant frequencies (as shown in figure 1
). A Fourier transform is a technique by which all the frequency components present in the ultrasonic signal are separated out and shown in a plot of frequency versus the amount of frequency present in the signal.
The inspection of small precious-metal items such as coins, regardless of material, presents some different challenges compared with the inspection of relatively large bars. The dimensions of the objects may vary considerably, in some cases being comparable in size with, or smaller than, the transducers we wish to use. Although specialist piezoelectric transducers can be made with very small “footprints”, they may not be ideal for these measurements for reasons we will discuss later.
In addition to the surface size of the object, the thickness of material beneath the transducer can be critical for ultrasonic inspection. In some cases the objects will be of sufficient thickness that a pulse-echo measurement (for example) may yield a series of discrete echoes, but for thinner items, all the echoes may overlap together, making meaningful time-domain analysis impractical. In addition it must be assumed that the surfaces of items such as coins and jewellery will normally be covered with a high degree of fine detail that will tend to scatter the ultrasonic waves, increasing attenuation and reducing useful signal.
Fortunately, there is an alternative to analysing the signal from such objects in the time domain and trying to distinguish individual echoes. A Fourier transform can be performed on the ultrasonic signal detected, converting the signal into a frequency spectrum, which is a measure of the relative amplitude of each possible frequency component of the wave.
Each frequency corresponds to a unique wavelength of the ultrasound, and because the object being studied is of comparable size to these wavelengths, only wavelengths where each subsequent reflection arrives at the same surface in phase are supported by the object. These are known as the resonant modes of the object, and are analogous to the resonances used by most musical instruments to achieve particular notes. Since the dimensions of the object are known, the relationship between these dimensions – which define the wavelength of the resonant modes – and the measured frequency will give the velocity in the specimen, which can be used to infer the presence of impurities as previously described.
A single transducer operating in pulse-echo mode, generating a broadband pulse of ultrasound is the simplest practical solution for resonant mode measurement. By looking at the spectrum of frequencies that the specimen resonates at, we can find out the velocity of sound in it that can be used as an indicator of the metal alloys present throughout the material. Also, we can look at how quickly the sample stops “ringing” after the ultrasound is put into it, which can provide information about its internal structure.
Measuring the resonant modes of a small sample is a very high-precision task, and great care must be taken not to allow the size and weight of the ultrasonic transducers to distort the result: normal transducers must be in contact with the sample to work, and if they are much bigger and heavier than the sample they may influence the frequencies that it rings at. One option to minimise any distortion might be to use non-contact ultrasonic probes such as lasers or electromagnetic acoustic transducers (EMATs). Also, specialist computer software is required to analyse the frequency spectrum of the signal and calculate the attenuation (the rate that the ringing dies down).
 Nondestructive evaluation of cylindrical components by resonance acoustic spectroscopy, F. Honarvar, A.N. Sinclair, Ultrasonics Vol. 36, 1998, pp. 845-854.
 The Measurement of Ultrasonic Attenuation, E. P. Papadakis, Ultrasonic Measurement Methods (Physical Acoustics Vol. XIX), (c) 1990 Academic Press Inc.