There are two audio circuits for generating sound. They are identical but completely independent and can be operated simultaneously to produce sound effects through the TV speaker. Each audio circuit has three registers that control a noise-tone generator (what kind of sound), a frequency selection (high or low pitch of the sound), and a volume control.
The noise-tone generator is controlled by writing to the 4 bit audio control registers (AUDC0, AUDC1). The values written cause different kinds of sounds to be generated. Some are pure tones like a flute, others have various "noise" content like a rocket motor or explosion. Even though the TIA hardware manual lists the sounds created by each value, some experimentation will be necessary to find "your sound".
Frequency selection is controlled by writing to a 5 bit audio frequency register (AUDF0, AUDF1). The value written is used to divide a 30KHz reference frequency creating higher or lower pitch of whatever type of sound is created by the noise-tone generator. By combining the pure tones available from the noise-tone generator with frequency selection a wide range of tones can be generated.
Volume is controlled by writing to a 4 bit audio volume register (AUDV0, AUDV1). Writing 0 to these registers turns sound off completely, and writing any value up to 15 increases the volume accordingly.