Tunnel effect for ultrasonic waves in tapered waveguides

Traversal time in tunneling effect for ultrasonic waves in tapered waveguides is derived considering its analogy with quantum and electromagnetic waves tunneling. If, as traversal time, the so called phase time is considered, the ultrasonic wavepacket shows the equivalent in acoustics of superluminality i.e. the derived velocity , crosses the limit of bulk transverse ultrasonic waves in the medium of the waveguide that is the equivalent of c in the quantum and electromagnetic cases. Graphs clearly illustrating this so called Hartman effect are obtained confirming the experimental results in the three different fields.