When we send white light through a prism, the light is decomposed in the colors that constitute it due to the different velocities which different frequencies. Is there a way to decompose "white sound" (in which all hearable frequencies are present just as in white light all visible colors are present) into its constituting waves? or will this automatically happen when such a wave travels through the air. If so, will we hear different sounds when we listen to the dispersed wave? Say a tone that increases in height, from the lowest hearable frequency to the highest?
More or less, this is what happens inside the human ear. The cochlea is shaped to lead to different frequencies resonating in different parts of the space. It is how we separate out different frequencies. This is the same as a prism, in that different frequencies are mapped to different locations.