Coherent speckle is a source of image noise in ultrasonic B-mode imaging. The use of multiple imaging frequencies has been suggested as a technique for speckle contrast reduction. This technique involves the averaging of images whose speckle patterns have been modified by a change in the spectrum of the transmitted or received acoustical pulse. We have measured the rate of this speckle pattern change in ultrasonic images as a function of the change in center frequency of the transmitted acoustical pulse. This data is used to quantitatively describe the trade-off of resolution loss versus speckle reduction encountered when frequency compounding is employed and to derive the optimal method of frequency compounding. These results are then used as a basis for describing the overall advisability of frequency compounding in ultrasonic imaging systems. Our analysis indicates that simple frequency compounding is counterproductive in improving image quality.