We studied the amplitude modulation of Langmuir waves in the process of electron-beam interaction by performing particle-in-cell computer experiments. Without applying the conventional nonlinear theories such as the decay instability and the modulation instability, we confirmed that the amplitude modulation observed in the computer experiments can be accounted for by nonlinear trapping theory which explains the spatial scales of the modulation with nonlinear electron trapping in electrostatic wells. In order to apply the nonlinear trapping theory to observational data, we modified the theory to be applicable to temporal data. We basically confirmed the agreement between the theoretical estimate and the temporal scale of wave packets observed in the computer experiments. We found that temporal waveforms obtained in the computer experiments are quite similar to those observed by the Geotail spacecraft. By applying the theoretical estimate of temporal scales of wave packets to the Geotail wave data, we found that the phase velocity of the excited Langmuir waves, which is close to the electron beam velocity, can be roughly estimated with time resolution much higher than the particle observation.