We have investigated the sound propagation in ${\mathrm{SiO}}_{2}$ aerogels and three types of organic aerogels: resorcinol formaldehyde, melamine formaldehyde, and vitreous carbon. The main parameter determining the sound velocity is the aerogel density; however, the bond strength and cross linking also influence the stiffness of these materials. Furthermore, we show that at least two types of low-density aerogels become less stiff and consequently the sound velocity is lowered when the specimens are uniaxially compressed. We explain this in terms of a model for the internal structure.