Abstract: In the apparatus disclosed herein, a bone containing body member to be tested is placed between a pair of transducers and a predetermined sequence of tone signals having frequencies spanning a range from 200 to 600 kilohertz is transmitted through the body member, and the set of values representing the amplitudes of the corresponding received signals are stored. The set of values obtained with the body member between the transducer is normalized using a set of values obtained from the same sequence without the body member in place thereby to generate a third set of values which are compensated for the response characteristics of the transducer and related interfaces. A value corresponding to the rate of change of attenuation with respect to frequency is then calculated from the third set of values and is adjusted for the bone thickness, this adjusted value being related to characteristics of the body member. The bone thickness is determined by a broadband pulse echo measurement.