摘要:

A study of the complete equation expressing the action of a driving force, periodic in time but constant throughout the length of the string and opposed by a damping force proportional to the velocity, leads to formulae suitable for the practical calculation of the shape of standing waves that are produced by a plane wave of sound or by a steady wind. At resonance the amplitude at the midpoint of a uniform string set into a plane wave of sound is proportional to the diameter, to the square root of the intensity of the wave (G erg per sq. cm. per sec.), and inversely proportional to the order of the overtone and to the square root of the frequency. Damping causes the lag between force and motion to differ from point to point, particularly near the nodes, so that even at resonance the wave pattern is not rigorously stationary. On the average, the lag increases from the value zero, obtained when the ratiov/v0between applied frequency and fundamental frequency is zero, to ±π/2 whenv/v0 = 1, increases again from −π/2 through 0 atv/v0 = 2, to π/2 atv/v0 = 3, and so on.

ISSN:1923-4287    

DOI:10.1139/cjr39a-001

出版商:NRC Research Press    

年代:1939

数据来源: NRC