The Hall MHD reconnection processes with various plasma β （the ratio of plasma pressure to the magnetic pressure） are numerically studied. The reconnection rate A/ t｜st at the quasi-steady state is in the range of 0.15 ≥ A/ t｜st ≥ 0.095 for the cases with plasma β ranging 0.5 ≤ β ≤ 6.5. In this report, the waves in the Hall MHD reconnection are investigated： The time series of the out-of-plane magnetic field By and the velocity components vx, vz in the xz plane at the given points are transferred into the power spectra by the Fast Fourier Transformation （FFT） for the cases with various plasma β. The results indicate that the frequencies of the By, vx, vz power spectra are in the range of Ωci 〈 ω 〈 8Ωci where Ωci is the proton cyclotron frequency. A shift to low frequency and the energy reduction at the peaks in the power spectrum can be found as the plasma β increases. Using the Minimum Variance Analysis （MVA） on E, the propagation directions k of the waves are determined. The angles α between the wave vector k and the local magnetic field B increase with increasing β： For case 3 with the largest （β = 6.5） α 〈 28°, so that k is approximately parallel to B. In order to investigate the polarized features of waves the hodographs of E are plotted in the plane perpendicular to the wave vector k. The hodographs for all three cases illustrate a right-hand circularly polarized feature. In case 1 with β = 0.5, it is a right-hand elliptical polarization, but in case 2 （β = 2.5） and case 3 （β = 6.5） the hodographs become a complicated right-hand circulation. Such wave behaviors are the signatures of whistler wave, and so the present work might provide a link between the fast reconnection rate and whistler wave.
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