Analytic relations between acoustic relaxation frequency and external temperature and pressure in multi-component excitable gases are deduced. Theoretical and calculational results show that relaxation frequency is inversely proportional to relaxation time of primary relaxation process, proportional to vibration coupling heat capacity of primary relaxation process, and inversely proportional to external heat capacity. Increase of temperature is related to increase of heat transfer capacity and energy transfer rate of internal and external degrees of freedom, which leads to decrease of relaxation time. It results that relaxation frequency is proportional to ambient temperature. Increase of pressure increases molecular collision rate and causes relaxation time to decrease, which brings about relaxation frequency being linearly proportional to ambient pressure.