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During the Sediment Acoustics Experiment in 1999 (SAX99), the in Situ Sediment geoAcoustic Measurement System (ISSAMS), transmitting tone bursts containing an integer number of cycles, was used to measure the speed and attenuation of compressional waves in a weakly dispersive, medium-sand sediment in the Gulf of Mexico. ISSAMS was deployed at seven stations and operated mostly at a frequency of 38 kHz, but at two of the sites, a succession of pulses was transmitted with frequencies extending from 25 to 100 kHz, in 5-kHz increments, yielding the phase speed, the group speed and the attenuation as a function of frequency. An analysis of a tone-burst transmission in a dispersive medium illustrates that several subtle factors, including the narrow bandwidth of the source, along with dispersion and attenuation in the medium, have the potential for introducing significant errors into travel-time measurements. It is concluded that, in general, the timing is best performed between two receivers rather than between the source and a receiver, the difficulty in the latter case being that the output from a narrow-band source is not a replica of the input. A correlation applied to the arrivals at the two receivers yields the travel time, from which a good approximation to the group speed is immediately available. Alternatively, a Fourier decomposition yields the phase speed as a function of frequency, which would be an advantage in a highly dispersive medium. The two techniques return almost identical wave speeds when applied to the ISSAMS tone-burst data from the weakly dispersive SAX99 sediments: at 38 kHz, the mean wave speed from the six primary stations is 1778 m/s. Attenuation was also estimated from receiver-to-receiver travel paths, using three different techniques: the ratio of the mean-square values of the arrivals, the ratio of the Fourier magnitudes of the arrivals and transposition. All three methods yield similar results when applied to the SAX99 data, returning a mean attenuation from the six stations of 12 dB/m at 38 kHz, which is comparable with previously reported measurements of attenuation in marine sands. From the broadband measurements, between 25 and 100 kHz, the dispersion is found to be weak but detectable and the attenuation scales almost linearl- y with frequency, which corresponds to a nearly constant Q.