This work shows the effect of the drive point impedance of a finite acoustic system on the power delivered by a realistic source. At low frequencies when the modal overlap of the system is small, the frequency‐averaged power delivered by the source can be much less than the power which the source would deliver to an equivalent semi‐infinite system. An analysis of the power flow into a finite one‐dimensional wave tube is used to explain the observation that broad‐band high‐intensity acoustic drivers deliver less low‐frequency power to small reverberation chambers than they deliver to progressive wave tubes. The analysis indicates that the modal overlap also plays a central role in the determination of the ratio of space‐averaged to drive point response.