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Angular Distribution of the Acoustic Radiation from a Tuning Fork

 

作者: R. M. Sillitto,  

 

期刊: American Journal of Physics  (AIP Available online 1966)
卷期: Volume 34, issue 8  

页码: 639-644

 

ISSN:0002-9505

 

年代: 1966

 

DOI:10.1119/1.1973192

 

出版商: American Association of Physics Teachers

 

数据来源: AIP

 

摘要:

It is shown by elementary arguments that the familiar loudness distribution pattern in the immediate neighborhood of a tuning fork is not, as is often suggested in elementary texts, due to pathlength-dependentphasedifferences between the waves reaching the ear from the different faces of the prongs, but to pathlength-dependentamplitudedifferences. At great distances from the fork, however, amplitude variations become negligible and pathlength-dependent phase differences give rise to a quite different loudness distribution pattern. From an idealized model, which represents a tuning fork as four colinear sources of strengths +B, −B, −B, +B, the velocity potential is calculated and the mean-square-pressure and intensity distributions are derived. It is shown that the mean-square-pressure distribution depends on polar angle(θ)and distance(R)as(3 cos2θ − 1)2/R6close to the fork—the easily audible (amplitude-dependent) nearfield pattern; and ascos4θ/R2at great distances—the less familiar (phase-dependent) farfield case. The intensity distribution comprises acos4θ/R2radial outward flow with, superposed, a circulation of energy from equatorial(θ ≈ 90°)to polar(θ ≈ 0,thinsp;180°)regions, varying with distance as1/R4. There are two zeroes of intensity: whereR = 0.225λ,θ = 0and 180°. The power radiated is estimated for a typical 520 cps fork, and is found to be2.5 × 10−15W when the prongs vibrate with an amplitude of 0.2 mm.

 

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