Packets of cnoidal internal waves were observed during a shallow-water experiment in the Gulf of Mexico. They lasted about 3 h and were always observed at the same time of day, clearly in response to tidal forcing. The cnoidal waves had 2--10 m amplitudes, narrow frequency bandwidths with central frequencies of about 9 cph, wavelengths of about 435 m, and they propagated in the along-slope direction. Data from a set of three thermistor arrays were processed to obtain directional wave spectra. These spectra establish the strong directionality of the cnoidal wave packets. The background ``continuum'' spectrum is resolved into a small set of discrete, strongly directional components. Observations of low-frequency acoustic propagation along several baselines showed fluctuations induced by cnoidal waves. These effects were simulated using a time-step PE approach. A mode-coupling resonance with the internal wave field results in elevated acoustic variability along a set of discrete spokes, emanating from the acoustic source. While acoustic variability tends to increase with range and with internal wave amplitude, tangential and radial correlation scales do not show a systematic dependence. Other implications of relative directionality between internal wave and acoustic propagation are discussed.