Question: after studying alternating current waveforms halfwave rectification and capacitor smoothing...

After studying alternating current waveforms, half-wave rectification and capacitor smoothing, a student proposes the following hypothesis:

The peak-to-peak value of the ripple voltage obtained with a capacitor smoothed, half-rectified sinusoidal waveform is proportional to the logarithm (base 10) of the value of the smoothing capacitor used.

Design an experiment to verify the hypothesis above