Acoustic impedance (Z) indicates how much sound pressure is generated by the vibration of molecules of a particular acoustic medium at a given frequency. This frequency (f) dependence is useful when describing the behaviour of musical wind instruments. Mathematically, it is the sound pressure p divided by the particle velocity c and the surface area S, through which an acoustic wave of frequency f propagates. This is a longwinded way of saying that the specific acoustic impedances must match for maximum transmission. If they don’t, there’s too much reflection and not enough transmission. This is one reason why during prenatal ultrasound scans, a gel is placed on the transceiver to provide good acoustic coupling as well as lubrication. Here’s the formula
Poor acoustic coupling. This is a problem between middle and inner ear because they don’t match acoustically. z (air) in the middle ear and z for the cochlear fluid is very different, hence a lot of the sound doesn’t get transmitted into the cochlear fluid. This is why the middle ear needs to amplify the sound first.
Since density is involved, temperature changes affect z. Higher temperature means higher speed and lower density. Since speed predominates, the higher the temperature the smaller z.