We report measurements of the hydrostatic pressure dependence of the e
lastic constants of poly(methyl methacrylate) using high resolution Br
illouin spectroscopy. We have measured the density rho(p) up to 500 MP
a, and the longitudinal and transverse sound velocities up to 300 MPa.
We have calculated the bulk modulus, Youngs modulus, shear modulus an
d Poisson's ratio. Initially there is a strong increase in the intensi
ty of the shear phonons which levels off at p > 100 MPa. At this press
ure a dispersion-like step in the shear modulus as well as a decrease
in the bulk modulus is found, which is tentatively discussed as a 'wea
k glass transition' within the glass.