The pressure standing waves in a brass musical instrument have a pressure anti-node at the mouthpiece end. This indicates that the lips effectively close the mouthpiece end of the instrument. If the air column of the instrument was cylindrical then the resonance frequencies would be the odd components of the harmonic series. However, brass instruments have internal profiles which expand along their length meaning that the mode frequencies are raised, with the lower modes being raised to the largest extent. The flare of the bell is designed to bring the resonances into an approximately harmonic relationship. The exception is the lowest resonant frequency which is lower than it would be for a true harmonic relationship in instruments with a significant amount of cylindrical tubing such as the trumpet and trombone.
As discussed previously, an oscillating volume velocity is put into the instrument through the lips to support the resonance. A small fraction of the energy in the pressure oscillations in the instrument's air column will be transmitted out to the surrounding air. These pressure waves are audible to the player and listeners as musical notes at the pitch corresponding to the frequency of the excitation. Valves and tuning slides are often included to enable the player to alter the length of the air column and therefore change the resonances.
Sound can be produced by skilled players at any of the resonant frequencies or at a frequency slightly away from a resonance by careful control of lip tension. It should also be noted that the velocity source at the lips will in practice have many harmonically related frequency components. The amplitude of the impedance at these frequencies will then influence the pitch and harmonic content of the resulting sound. For instance, well-tuned, harmonically related resonance peaks will mean more harmonic content and a brighter tone.
If the frequencies present in the excitation are all well away from resonant frequencies, very low sound levels will result and in practice the reflections of sound within the instrument will force the lips of the player to change their oscillations to play at a frequency where components of the excitation are supported by air column resonances. As mentioned before, the resonance frequencies of the trumpet and trombone are close to being harmonically related, except the lowest resonance which is flat (ie. lower in frequency than would be required for a harmonic relationship). If the player excites the instrument at the frequency of this bottom resonance the note is weak because the upper harmonics are not supported by resonances. However, if a note is played such that the harmonics in the excitation match the harmonically related resonances, the note is strong. This is known as the pedal note. Note that the pitch perceived by a human listener is the same as that for a sinusoidal oscillation at the fundamental of the harmonic series even when the component of the fundamental actually present in the sound is very weak.
In order to characterise the behaviour of an instrument we use a frequency dependent quantity called the input impedance. The input impedance is the ratio of the pressure and volume velocity at the input or mouthpiece end. In terms of brass instruments this means the input impedance gives a measure of the sound pressure amplitude in the mouthpiece due to a given amplitude of sinusoidal excitation created by the varying flow of air between the lips. A plot of input impedance against frequency will have peaks at the resonance frequencies. The sharpness of the peak also indicates information a player can recognise. The sharper a peak is, the easier the resonance will be to play and the more difficulty a player will experience in attempting to play at a frequency slightly away from the resonant frequency.