PUB - Publikationen an der Universität Bielefeld

We calculate the speed of sound c (s) in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form rho(m)similar to m (-a) exp {bm}, which leads to singular behavior at the critical temperature T (c) =1/b. With a=4 the pressure and the energy density remain finite at T (c) , while the specific heat diverges there. As a function of the temperature, the corresponding speed of sound initially increases similarly to that of an ideal pion gas, until near T (c) resonance effects dominate, which causes c (s) to vanish as (T (c) -T)(1/4). In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around T (c) , the actual critical behavior in these models is no longer present.