A measurement of the electric field wave spectrum by the S3-3 satellite has shown the upper frequency cutoff of the whistler mode wave to be below 16 kHz. This measurement shows that the electron density in the polar cap can be as low as 1 cm-3 at 7000 km. However, since the measurement is unique in the examined data set of the S3-3 satellite, such low densities must be rare both in the polar ccap and in the auroral zone, except perhaps in regions of upgoing ion beams where whistler mode waves are usually not detected. This low density was confirmed by a measurement of the local lower hybrid frequency. The spin modulation of the wave amplitude as a function of frequency was used to determine that the wave was propagating down the magnetic field line.