A new experimental method has been developed for studying coupled plasmon-ripplon resonances of electron crystal formed on the surface of liquid helium. Measurements are done at temperatures between 0.45 and 0.9 K and electron areal densities from 5 ×10 8 to 1.2 ×10 9 cm -2 . Resonance frequencies are quantitatively compared with the theory by Fisher, Halperin, and Platzman (FHP) and by Namaizawa. The agreement between the experiment and the FHP theory is satisfactory at low electron densities, although at high densities a modification is needed. The Debye-Waller facfor of the Wigner crystal is well explained by the Debye model, and the factor is found to have a significant contribution from the zero-point vibration of the Wigner crystal.