The purpose of an audio mixer in a sound system is to control and balance multiple audio signals. It allows the user to adjust the volume levels, tone, and various other parameters of each individual audio input and output. The mixer combines different audio sources such as microphones, instruments, and recorded sounds into a unified audio output. It also enables the user to create a mix by blending different audio sources together and applying various effects and processing techniques. Ultimately, the audio mixer plays a crucial role in achieving a balanced and professional sound output in live performances, recording studios, and other audio production environments.