The PA (Public Address) system is composed by a band-pass filter from $300$ $\mathrm{Hz}$ to $3$between a range of frequencies $\mathrm{kHz}$.$f \in [f_i , f_f]$
The quality of the sound is affected because the voice frequencies may exceed this range and thus, the band-pass filter rejects these peaks, that are exceeding the filter range.
Remember how a band-pass filter works:
The frequencies below $300$ $\mathrm{Hz}$$f_i$ are not allowed nor the frequencies above $3$ $\mathrm{kHz}$$f_f$. Nevertheless, when the frequencies are outside of the bandwidth range (determined by the $\Delta f=f_2-f_1$ at which the gain has a value of $\mathrm{gain_{max}}-3$ $\mathrm{dB}$), the quality of the sound gets worse and therefore, from the cabin we are listening to a dimmed sound of the flight crew voice.
Some of the newer aircraft PA systems are done by using DSP (Digital Signal Processing) systems, also within the limited range, but the quality of the sound is more improved.
References: Dimov Stojce Ilcev, "Global Aeronautical Communications, Navigation and Surveillance (CNS)", June, 2013.