is defined as
Z(f) = P(f)/U(f), where P(f) and U(f) are sinusoidal quantities of pressure and volume flow, respectively.
An air column's input impedance is defined as its sinusoidal pressure response to a driving sinusoidal volume velocity source at the input to the air column.
An air column's impulse response is defined as its time-domain pressure response to the application of a volume velocity unit impulse at the input of the system.
The impulse response and input impedance of an air column are time- and frequency-domain correlates, as shown in Fig. 1 below.
Theoretical input impedance magnitude (top) and impulse response (bottom) of a cylindrical bore, normalized by the bore characteristic impedance.
The input impedance peaks indicate the frequencies at which a volume velocity source will produce the greatest pressure variations at the input to the air column.
The input impedance minima indicate the frequencies at which a pressure source will produce the greatest volume velocity variations at the input to the air column.
For pressure controlled driving mechanisms (such as the brass player's lips), the input impedance peaks indicate the frequencies at which air column vibrations will cooperate with the driving mechanism to sustain steady oscillations.
In the past, input impedance was measured using a variable-frequency volume velocity source of constant amplitude. However, time-domain and multi-microphone measurement techniques have become popular during recent years.