Angular Distribution of the Acoustic Radiation from a Tuning Fork

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-dependent phase differences between the waves reaching the ear from the different faces of the prongs, but to pathlength-dependent amplitude differences. 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/R6 close to the fork—the easily audible (amplitude-dependent) nearfield pattern; and as cos4θ/R2 at great distances—the less familiar (phase-depe...