The sunspots are widely used to measure the rotational rate of solar surface. We are interested in analysis of the temporal evaluation of the short-term period present in sunspot time series (i.e. sunspot number and area) during the ascending phase of Solar Cycle 24. For the better understanding of variation in solar activity originated at different layers of the solar atmosphere with respect to sunspot cycles, we study the phase relation between sunspot numbers and sunspot areas using cross correlation analysis techniques based on extended wavelet based approaches such as continuous wavelet transform, cross-wavelet transform, and wavelet coherence. In this study we found the short-term periodicity “27 days-rotational rate of Sun” for current solar cycle 24 (January2008-May2013), which suggested that the Solar Cycle24 has minimum solar activity. We have also investigated the correlation between both parameters and identify the unusual conditions in space weather.