Resonance phenomena were observed of a thermally excited phonon confined in a very small space. The power spectrum changes due to the boundary condition of the cavity shape. A cylindrical cavity which has a 1450-(mu)m inner diameter containing water was prepared as a sample. The resonance frequency in the cylindrical cavity is given by a solution of Bessel's function. An optical beating system is used which has a hyperfrequency resolution to detect this fine structure of the resonance spectrum. The spatial decay of phonons is very large in the liquid sample. The low-frequency measurement is required to observe the resonance phenomena, because the phonon can reflect many times in the cavity. Generally though, a broadening of the wave vector due to angular divergence of the laser light is very large in a small-angle light-scattering measurement, since the wave vectors of the resonance peaks are determined only by a boundary of the cavity. Several resonance peaks can be observed around the 8 MHz measurement and a typical peak width is 50 kHz. The strong peaks are observed at every 500 kHz. These peaks are the symmetric and lowest asymmetric tangential modes.