Francis M. Wiener

Sound Diffraction by Rigid Spheres and Circular Cylinders

The results of calculations of the pressure distribution on the surface of a stationary rigid sphere and a stationary rigid circular cylinder of infinite length, when exposed to a plane progressive sound wave, are compared with experiment. A small probe microphone was used to measure the sound pressures on the surface of the obstacles in a room essentially free from acoustic wall reflections under a variety of experimental conditions. The sound pressures p on the surface are conveniently expressed relative to the free‐field pressure p0 in the undisturbed incident wave.In the case of the sphere, reasonably good agreement was obtained between theory and experiment in the range of 13 <ka < 10, where k is the wave number of the incident wave and a the radius of the obstacle. In particular, the existence of the “bright” spot diametrically opposite the point nearest the sound source was verified experimentally. This comparison of experiment with theory affords a valuable means of estimating the validity of the ...

The Diffraction of a Progressive Sound Wave by the Human Head

The increase in sound pressure at the eardrum over the free‐field pressure in a progressive sound field is caused by a combination effect of diffraction by the head and pinna and resonance in the auditory canal. In an earlier paper the pressure distribution in the auditory canal was determined on a number of subjects in a plane progressive sound field. Expressed in terms of the ratio of the sound pressure at the eardrum to that at the entrance of the ear canal, it was found to be essentially independent of the orientation of the observer with respect to the sound source, as might be expected from theory. This fact makes it possible to separate the two effects and to measure the diffraction by the head by inserting a probe microphone near the entrance of the ear canal and comparing the sound pressure measured there with the free‐field pressure. To the obstacle effect of head and pinna, so determined, the pressure increase due to resonance in the auditory canal is to be added. The subjects were placed in fr...

On the Intelligibility of Bands of Speech in Noise

Articulation tests were conducted with a large number of communication systems having band widths ranging from about one‐half octave to a system covering the entire range of speech frequencies. The systems were linear and their responses were approximately uniform over the pass band, with sharp cut‐offs at either end. The acoustic gain of the systems was expressed relative to the transmission of speech through one meter of air between talker and listener. Two spectra of masking noise were used, and each system was tested over a wide range of speech‐to‐noise ratios. In one group of experiments the speech was filtered before mixing with noise and in the other group both the speech and the noise were passed through the same filter. For each of the band‐pass systems a relation between syllable articulation and level of received speech was obtained. From these gain functions, families of equal‐articulation contours may be derived. These contours show, for example, how the gain must be changed for a given chang...

The Diffraction of Sound by Rigid Disks and Rigid Square Plates

A rigid circular plate was exposed to an essentially plane progressive sound wave, and the sound pressure p at various points on the surface measured relative to the free‐field pressure p0 in the undisturbed incident wave by means of a small probe microphone. The diffraction effect |p/p0| was determined as a function of angle of incidence over a range of frequencies beginning with “long” wave‐lengths and extending into the region where the radius a of the obstacle approximately equals the wave‐length. Expressed in customary notation, 14 < ka < 8, where k is the wave number of the incident wave. Data were obtained for angles of incidence θ = 0, 45, 135, and 180 degrees, where θ is measured with respect to the axis of the obstacle. Similar measurements for θ = 0 and 180° were made for a rigid square plate with side 2a.Approximate contour maps of the quantity |p/p0| in decibels have been prepared from the experimental data portraying the pressure distribution on the surface of the plates.The experimental results are compared with computed values of |p/p0| obtained from an approximate theory in which an attempt is made to solve the problem in terms of a scattered potential calculated as if the face of the obstacle were surrounded by an infinite baffle. The agreement is quite good on the “illuminated” side of the plates, i.e., for θ = 0 and 45° and on the “shadow” side for θ = 180°. The agreement for 135 degree incidence is generally poor, although the computed values show the trends of the experimental data in many instances. At low frequencies the theory gives values which are somewhat too high on the illuminated side and too low on the shaded side.The values of |p/p0| obtained from the exact expression of the diffraction of a plane wave by a disk of zero thickness and for perpendicular incidence are found to be in good agreement with experiment and the approximate theory on the illuminated side (θ = 0) and they agree reasonably well on the shaded side (θ = 180°) for 1⩽ka⩽5. The region near the edge shows discrepancies which are to be expected from the finite thickness of the circular plate (approx. a/12).It is concluded that the approximate theory mentioned above is capable of predicting the diffraction effect |p/p0| on the illuminated side of the obstacles in the frequency range covered by this study for the angles of incidence investigated. On the shadow side the theory can be expected to yield usably approximate answers only for θ = 180°. There are reasonable grounds for the assumption that similar predictions can be made for points on or “near” the surface of “thin” plane obstacles of arbitrary shape and for other acute angles of incidence not too close to θ = 90°.A rigid circular plate was exposed to an essentially plane progressive sound wave, and the sound pressure p at various points on the surface measured relative to the free‐field pressure p0 in the undisturbed incident wave by means of a small probe microphone. The diffraction effect |p/p0| was determined as a function of angle of incidence over a range of frequencies beginning with “long” wave‐lengths and extending into the region where the radius a of the obstacle approximately equals the wave‐length. Expressed in customary notation, 14 < ka < 8, where k is the wave number of the incident wave. Data were obtained for angles of incidence θ = 0, 45, 135, and 180 degrees, where θ is measured with respect to the axis of the obstacle. Similar measurements for θ = 0 and 180° were made for a rigid square plate with side 2a.Approximate contour maps of the quantity |p/p0| in decibels have been prepared from the experimental data portraying the pressure distribution on the surface of the plates.The experimental res...

On the Relation between the Sound Fields Radiated and Diffracted by Plane Obstacles

In the past, acoustic diffraction and radiation problems have been treated separately in many cases, although their intimate connection is clear from theoretical considerations. This connection becomes a useful equivalence in the case of plane piston radiators and rigid scatterers exposed to an incident plane wave. This equivalence is of practical importance since it permits, with a minimum of effort, the transition from a problem in acoustic radiation to the related diffraction problem, and vice versa, where plane surfaces are involved. The foregoing principles are applied to the important case of the circular disk.

In Search of the Missing 6 Db

The unexplained difference in sound pressure in the ear canal which appears to exist when equally loud low frequency tones are presented alternately from an earphone and from a loudspeaker has bedeviled acousticians for many years and, unfortunately, still continues to do so. There are presented here the results of some of the measurements carried out at the Bell Telephone Laboratories which show the magnitude of the effect and various attempts at explaining it. While no satisfactory explanation has been found, it is hoped that publication of these results will stimulate interest in the problem.

Sound Measurements for Psychophysical Tests

The results of psychophysical tests on the auditory sensory system usually show much more variability than experiments involving only physical measurements of sound waves. This has resulted in the general impression that the variance of measurements of the auditory threshold and other psychoacoustic measurements is largely due to the inability of the observers to give consistent responses. This paper reports the results of a series of threshold measurements made under carefully controlled conditions and accompanied by search tube measurements of the sound pressures in the ear canals of the observers. The small variances obtained under certain conditions suggest that the large variability oftentimes experienced in psychophysical work is partly due to inadequate techniques for measuring the levels of the stimuli that activate the sensory system.

Notes on Sound Diffraction by Rigid Circular Cones

A stationary right circular cone was exposed to an essentially plane progressive wave, and the sound pressure p at various points on the surface was determined relative to the free‐field pressure p0 in the undisturbed incident wave. Measurements were made in the frequency range of 14  90°. A “bright” spot appears at the center of the base when the vertex points directly towards the source (θ = 180°). For incidence normal to the base, pressure measurements have been made at several other points on the surface of the cone...

Phase Distortion in Electroacoustical Systems

In the course of an investigation of phase distortion in electroacoustical systems the phase shift vs. frequency characteristic of a standard miniature condenser transmitter was measured by application of the principle of reciprocity. Measurements were made in a closed cavity and in free space. In analogy to the free field response the phase of the pressure in the undisturbed sound wave was taken as reference. By application of a principle of similitude the phase shift due to diffraction and cavity resonance was determined experimentally and found to be in agreement with theory. The phase characteristics of a number of commercial microphones of representative types were investigated by comparison with the standard condenser microphone. Difficulties were encountered at wave‐lengths comparable with the dimensions of the microphones due to the uncertainty of microphone position with respect to the source. Relative response curves were obtained as a supplement and general check on the experimental method. The...

Noise Levels Due to an Airplane Passing Overhead

The noise spectra and levels due to an airplane flying overhead in level flight have been measured near the ground. The results of such measurements for an airplane closely corresponding to the Douglas DC‐3 transport plane are discussed for altitudes between 100 and 500 feet and maximum engine power.