This paper addresses the perception of differences between sounds of trumpets played by a musician or simulated by physical modeling. The harmonic balance technique is used to simulate trumpet sounds in permanent regime. The input parameter of the simulations is the input impedance of the trumpet (resonator), the control parameters are the characteristics of the virtual musician (excitator), and the outputs of the simulations are the playing frequency and the magnitude of the 6 first harmonics of the notes. Three different trumpets, obtained by small geodescriptoral variations of the leadpipe, are first simulated using several virtual musicians, and second played by a "real" musician. The objective of this paper is to define to which extent differences between sounds are noticeable by a panel of listeners. The factors of the experiment are the type of instrument used (type of trumpet), the playing dynamics of the sounds (pressure in the mouth for the simulated sounds), and the virtual musician (characterized by the control parameters of the simulations). For the two populations of sounds (simulated or real), a two alternatives forced choice hearing test was designed, with a panel of 26 participants. The analysis of the results of the tests with the signal detection theory allows the determination of the influence of the different factors on the noticeable differences between the sounds. The agreement between the results concerning the simulated sounds and the real sounds is assessed, to open the door to sound simulations for instrument design.