Understanding sound dispersion
The dispersion of sound depends on two parameters - the wavelength of the sound and the size of the source.
An ideal point source provides omnidirectional output at all frequencies because the size of the source is very small compared to the wavelengths of all the sounds, whilst a speaker of infinite diameter would produce a narrow beam of sound because the size of the source is very large compared to the wavelengths of the sounds.
So if we look at a typical speaker mounted in a cab we find that at low frequencies the output is omnidirectional - that means that if you stand behind the cab you will hear as much bottom as you will standing an equal distance in front of the baffle. At midrange frequencies the output goes solely forwards with lower mids being dispersed strongly to 90 degrees either side, and then higher midrange frequencies being projected in a gradually narrowing cone as the frequencies get higher (and thus the wavelengths get smaller) until the output is finally in a narrow beam.
For an ideal pistonic 15" woofer the beaming frequency is ~ 1kHz.