How is it possible to have an instrument like a bugle that has a fixed-air column play a melody?

The various notes are pitched by tightening and/or relaxing the lip muscles.

It's as simple as that? My lab is on speed of sound in air. Does it have anything to do with speed of sound in air?

The bugle is an interesting instrument because it has a fixed-air column, meaning it does not have any keys or valves to change the length of the tubing. Despite this limitation, the bugle can still play a melody.

The reason the bugle can play a melody is because it utilizes different harmonics of the vibrating air column to produce different pitches. When air is blown into the bugle, it creates a standing wave within the tube. This standing wave is made up of various harmonics, which are integer multiples of the fundamental frequency.

The bugle's design allows for the production of the fundamental frequency and a series of higher harmonics. By adjusting the embouchure (the shape of the player's lips) and altering the amount of air blown into the instrument, the bugler can manipulate the strength of the different harmonics.

To play a melody on a bugle, the bugler relies on a combination of manipulating the embouchure and controlling the airflow. By changing the lip tension, tongue position, and air pressure, the bugler can selectively amplify certain harmonics while dampening others. This manipulation of harmonics creates different pitches, enabling the bugler to play a melody.

It is important to note that the bugle's range is limited to the specific harmonics it can produce. Consequently, it is not possible to play all the chromatic pitches found in Western music. This limitation gives the bugle its distinctive sound and explains why it is commonly used in military ceremonies and signals, where its clear and piercing tone can be heard from a distance.