Transmission through a layer

Abstract

The transmission of ultrasound through thin air and liquid layers is considered. It is well known that ultrasound very poorly penetrates through a layer of air of thickness h l that is enclosed between two solids. If both media are equivalent and have a wave resistance of z , the layer with a wave resistance of z l is thin, h l � λ l is the wavelength in the layer, and the energy reflection coefficient is calculated by the Rayleigh formula The table lists the values of calculated by this formula for air and water layers in steel at a frequency of 2.5 MHz. The table shows that a very thin air gap (0.00001 mm) that simulates a flaw reflects ultrasound almost completely. The figure presents plots for reflection coefficient from an air layer in steel corresponding to ( 1 ) the- oretical data calculated by the Rayleigh formula and ( 2 , 3 ) experimental measurements (1, 2). The upper scale along axis x corresponds to the product of the air layer's (gap's) width by ultrasound frequency h l f , whereas the lower scale corresponds to the air-gap width h l in mm for the 2.5-MHz frequency. It is easily seen that the values at which the reflection coefficient increases sharply are by two or three orders of mag- nitude higher than the values predicted by the theory. What is the explanation for such a considerable difference? It was assumed to be due to inaccuracies in measurement of the ultrasonic wave's amplitude at the layer's edges. However, an amplitude measurement error by two or three orders is unlikely. It is possible that this difference can be explained by imprecision in the manufacture of the air gap, which may contain points where the surfaces contact each other. This assumption appears doubtable because the shapes of theoretical and experimental curves are very similar. It is very difficult to manufacture surfaces with a roughness of 10 -5 -10 -4 mm. It is known that Johansson gage blocks used as ultimate thickness standards have a grade-12 surface finish. This means that the maxi- mum surface roughness does not exceed 2 × 10 -4 mm.