Teaching ultrasonics using spreadsheets

Whenever an ultrasonic wave encounters a boundary between two media it is partially reflected and refracted, as any acoustic wave would be. Unlike light, the wave also undergoes mode conversion so that in the general case a single incident wave could produce two reflected waves and two refracted waves. The angles which define the path of the wave are determined by Snell’s law and are easily calculated. The relative amplitudes, on the other hand, require quite complicated formula when the angle of incidence is anything other than 0 degrees. This problem gets compounded when the angle of the incident wave goes beyond the first critical angle. At this point the angle of the refracted wave becomes imaginary and the equations to calculate the relative amplitudes become complex. This paper describes a tool that has been developed, using a spreadsheet, which performs the calculations for all incident angles. The user selects the media and the type of incident wave and the resulting waves are shown graphically as well as numerically. The tool was developed primarily as part of an undergraduate course on ultrasonic testing, but could be used more widely.