Final correction of the resonator length

The final correction of the resonator length is a term from wave physics . It is also important for tuning some musical instruments.

process

Resonators have a fixed, calculable fundamental frequency for sound waves . In the case of tubes, this depends on their length L. In the case of a tube that is open on one side, a small distance, the so-called end or opening correction ΔL, must be added in order to obtain the effective tube length for the resonance. For all resonators open on one or both sides, this means that they have to be shortened by this uniform final correction distance ΔL in order to achieve the desired pitch .

Physical interpretation

Standing waves can propagate in a pipe with an opening and are also reflected at the open end of the pipe. Inside the pipe, a flat wave moving back and forth spreads, but at the end of the pipe it penetrates into the outside space as a spherical wave . There it is reflected and runs back into the pipe. This reflection is incomplete because part of the sound energy is given off. Overall, the sound propagation behaves as if the reflection takes place at the point ΔL away from the pipe end. Therefore the value for the effective pipe length must be increased by the distance ΔL. This correction mainly depends on the radius R of the pipe, but is the same for all pipe lengths and frequencies.

Calculations resulted in different values ​​for ΔL: Hermann von Helmholtz found a value of π / 4 R in 1859 , John William Strutt, 3rd Baron Rayleigh , calculated a correction of 0.82 R in 1894 , Harold Levine and Julian Schwinger received a value of 0 in 1948 , 61 R . This was also confirmed by experiments.

application

The correction must be applied to each opening of a resonator. It also applies to the Helmholtz resonator . Musical instruments that use tubes include the marimba , flutes, and organ pipes .

literature

• Neville H. Fletcher, Thomas D. Rossing; The physics of musical instruments ., Ch 8.3. Springer Handbook 2001.