Planetary waves in the mesosphere are studied using observational data and models to establish their origin, as there are indications of their generation independently of waves in the stratosphere. The quantitative relationships between zonal wave numbers m = 1 (wave 1) and m = 2 (wave 2) were studied with a focus on the mid-latitude mesosphere at 50N latitude. Aura Microwave Limb Sounder measurements were used to estimate wave amplitudes in geopotential height during the 2020–2021 winter major sudden stratospheric warming. The moving correlation between the wave amplitudes shows that, in comparison with the anticorrelation in the stratosphere, wave 2 positively correlates with wave 1 and propagates ahead of it in the mesosphere. A positive correlation r = 0.5–0.6, statistically significant at the 95% confidence level, is observed at 1–5-day time lag and in the 75–91 km altitude range, which is the upper mesosphere–mesopause region. Wavelet analysis shows a clear 8-day period in waves 1 and 2 in the mesosphere at 0.01 hPa (80 km), while in the stratosphere–lower mesosphere the period is twice as long at 16-days; this is statistically significant only in wave 2. Possible sources of mesospheric planetary waves are discussed.