  The amplification of acoustic phonons in a superlattice in the presence of an
electric field $E =E_0 + E_1 cos(\omega t)$ has been investigated theoretically
and numerically by computational methods. The calculation is done in the
hypersound regime $(ql\gg 1)$ where the attenuation coefficient depends on the
phonon wave vector $ q =[-\frac{\pi}{q} \quad \frac{2pi}{q}]$ and the frequency
$\omega_q = 10^{12} s^{-1}$ . An inversion is attained where amplification far
exceeds absorption and the ratio $
frac\mid\frac{\Gamma/\Gamma_0\mid_{min}}{\mid\Gamma/\Gamma_0\mid_{max}}\approx
3$ . A high frequency build up of acoustic energy from noise (phonon spectrum)
is obtained by using specialized spectral techniques. This indicates an
amplification of the phonons generated in the terahertz range leading to the
possibility of obtaining a hypersound MASER.
