Eleven-year Schwabe cycle in solar activity is not yet fully understood despite of its almost two century discovery. It is generally interpreted as owing to some sort of magnetic dynamo operating below or inside the convection zone. The magnetic field strength in the dynamo layer may determine the importance of the tachocline in the model which is responsible for the cyclic magnetic field, but the direct measurement is not possible. On the other hand, solar activity also displays short term variations over time scale of months (Rieger-type periodicity), which significantly depend on solar activity level: stronger cycles (or more active hemisphere in each cycle) generally show shorter periodicity and vice versa. The periodicity is probably connected to Rossby-type waves in the dynamo layer, therefore alongside with wave dispersion relations it might be used to estimate the dynamo magnetic field strength. We performed the wavelet analysis of hemispheric sunspot areas during solar cycles 13–24 and corresponding hemispheric values of Rieger-type periodicity are found in each cycle. Two different Rossby-type waves could lead to observed periodicities: spherical fast magneto-Rossby waves and equatorial Poincare-Rossby waves. The dispersion relation of spherical fast magneto-Rossby waves gives the estimated field strength of >40 kG in stronger cycles (or in more active hemisphere) and <40 kG in weaker cycles (or in less active hemisphere). The equatorial Poincare-Rossby waves lead to >20 kG and <15 kG, respectively. Future perspectives of Rieger-type periodicities and Rossby-type waves in testing various dynamo models are discussed.