Acoustic Interfaces

Lower Impedance Inverts Echo

The sign of a pressure echo follows impedance order. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Reversing the impedance order changes the sign

The interface from 6 rayl to 2 rayl gives coefficient negative 1 over 2.

R=−48=−1/2R=\frac{-4}{8}=-1/2
Lower impedance reflectionThe negative sign is computed from impedance order.incidentreflectedtransmittedleft 6 raylright 2 raylR -1/2in 4 Paback -2 Pathrough 2 PaI back 4 W/m^2

The reflected pressure is inverted

Incident pressure 4 pascals times negative 1 over 2 gives negative 2 pascals.

4⋅−12=−2 Pa4\cdot \frac{-1}{2}=-2\ \text{Pa}
Inverted pressure echoPressure sign is a checked label, not prose.incidentreflectedtransmittedleft 6 raylright 2 raylR -1/2in 4 Paback -2 Pathrough 2 PaI back 4 W/m^2