Energetic (>24 kev) ion distributions are used to remotely sound an ion trapping boundary at the dayside magnetopause for two inbound crossings of ISEE-2 on days 347 and 312, 1977, at 0830 and 1100 LT. By applying single particle trajectory models to the observed temporal relationships between trapping boundary distance and orientation parameters, we conclude that longitudinal standing waves occur on the boundary, having typical wavelengths of 1500--3000 km, amplitudes of 500 km, and periods of 200--400 sec. The standing wave nodes move along the node axis with velocities 1.5 to 6 km/sec. The data are inconsistent with models of traveling waves moving tailward along the boundary.