The phonon spectra of unstrained and strained quasiperiodic semiconductor superlattices (QSSL) have been calculated using one-dimensional linear chain model. We consider two types of quasiperiodic systems, namely cantor triadic bar (CTB) and Fibonacci sequences (FS), constituting of AlAs, GaAs and GaSb of which the latter two have a lattice mismatch of about 7%. The calculations have been made using transfer matrix method and also with and without the inclusion of strain. We present the results on phonon spectra of two component CTB and two as well as three component FS semiconductor superlattices (SSL), thickness and order dependence on LO mode of GaAs, effect of strain on LO frequency of GaAs. The calculated results show that the strain generated due to lattice mismatch reduces significantly the magnitudes of the confined optical phonon frequency of GaAs.