  The irreducible representations of the extended Galilean group are used to
derive the symmetric and asymmetric wave equations. It is shown that among
these equations only a new asymmetric wave equation is fundamental. By being
fundamental the equation gives the most complete description of propagating
waves as it accounts for the Doppler effect, forward and backward waves, and
makes the wave speed to be the same in all inertial frames. To demonstrate
these properties, the equation is applied to acoustic waves propagation in an
isothermal atmosphere, and to determine Lamb's cutoff frequency.
