Why bows get stiffer and racquets get softer when the strings are added

The frame of a string instrument is subject to a large tension force when the strings are installed. Intuitively, one might expect that the frame would be stiffened by the strings. Experimental data and a theoretical analysis are presented to show that this is not generally the case. An archer's bow is much stiffer when it is strung, but a tennis racquet is softened when the strings are added. As a result, the mode frequencies for transverse vibrations increase for a bow and decrease for a racquet when the strings are added. The effect of the strings depends on the extent to which the frame is bent at equilibrium. [DOI: 10.1119/1.1376378]