The technical implementation of this method is illustrated in Figure 4.6.

4.3.2 Real signal behaviour

Since the transducers have a finite reflection coefficient, the pressure of the sound wave is not converted completely into electrical signals; a portion is reflected back. One technical solution is to excite the sound wave with pulse modulation, so that multiple reflections are separated in time from the useful signal. To describe the pressure amplitude completely, however, multiple reflections must be taken into account:

This representation of the transfer function reveals an interesting additional phenomenon. From experience, one would expect the sound wave to decay exponentially along the propagation distance x. In reality, a cosine function is superimposed on this process. Multiple reflections produce a so-called λ/2 ripple. For a small distance between transmitter and receiver, or for weak attenuation α in the investigated solution, the influence of the cosine term is greatest (Figure 4.7), because according to Eq. (4.23) the ripple is attenuated with 2α.

The previously mentioned technique of modulating the output signal with a rectangular pulse of duration τ = 2–10 μs suppresses multiple reflections entirely at larger transducer separations. The pulse duration must satisfy the following time-window condition:

To determine attenuation accurately, it is very important to know the response characteristic of the receiving system. The useful signal passes through several electronic instruments in the receiver branch (see Figure 4.9). First, the voltage U_E generated by the transducer is demodulated and amplified. The high temperature sensitivity of instruments of this kind alone produces anomalies in what should ideally be a linear amplification response. Consequently, the signal originating from the A/D converter …