The speeds of motion of compression waves through a 3m tall fluidized bed of 10nm silica particles and 75 micron FCC particles were determined by measuring the times of arrival of compression zones using light and a gamma ray densitometer, respectively. A correlation for the modulus of elasticity for each particle type was determined as a function of void fraction. Using a Kinetic theory type equations of state for particles, this experimentally determined modulus gives a value for the granular temperature for 10nm particles of approximately 1 meters per second squared. This value is close to that obtained by assuming the motion of the 10nm particles is due to collision with air molecules with no energy dissipation. The value of the granular temperature was also determined in a two dimensional fluidized bed by measuring the volume fraction distributions of 10nm silica particles. Granular temperatures were deduced for a one dimensional particle momentum balance using an ideal equation of state for particles which is similar to a barometric formula for gases. These granular temperatures agreed with the measurements obtained from wave propagation experiments.