Vibration of Stiff Piano Strings
Harvey Fletcher · The Journal of the Acoustical Society of America · 1962
This paper reviews the work on the theoretical aspects o[ the vibration of piano strings. For solid strings, it deals with 2 boundary conditions: namely, (1) when the string is pinned with knife edges but not clamped, and (2) when the ends are clamped. In an actual piano, the condition is somewhere between these two. The theory is developed so as to apply to wrapped strings. In this case, the stiffness restoring force is principally due to the solid core rather than to the wire wrapped around it. Experimental values of the partial frequencies of piano tones from an upright piano are compared to the theoretical values. The partial frequencies from any of the strings can be represented by the formula fn=nf0(1+Bn2)12, where n is an integer and f0 and B are constants which can be determined from any 2 experimental values of the partial frequencies f>n. These constants can also be calculated from the physical constants of the wire and its tension, provided the exact boundary condition is known. A comparison between the experimental and theoretical values of these constants is given.