Abstract: From the strict derivation of transverse vibration of string, the explicit solution of wave velocity is obtained. Through measuring the wavelength and eigen frequency of resonance, the experiment value of wave velocity is also obtained, which is well agreed with the theoretical value. The transverse vibration equation of beam is also solved exactly. The simulation of the problem which one end is clamped and the other is free, is performed. The expressions of first several resonant eigen frequencies and the sites of standing-wave nodes are obtained so as to get the general solution. Further, the fundamental frequencies and resonant frequencies of the previous order overtone of steel slender strips under different lengths are measured. The co-ordinates of standing-wave nodes are observed and equivalent to the theoretical results, and the Young’s modulus of the strips are calculated, which are well corresponded with standard values. Furthermore, the case of small radial vibration of ring is popularized. The resonant frequencies and wavelengths are also measured, and the elastic modulus of circular cross section ring are obtained, where are also accorded with the existing values. 

Key words: transverse vibration of string, transverse vibration of beam, radial vibration of ring, eigen frequency, Young’s modulus