Isadore Rudnick

The Propagation of an Acoustic Wave along a Boundary

The sound field of a point source near the boundary of two media cannot be obtained by an acoustic‐ray approach. In fact, such an approach which utilizes the reflection coefficient for plane waves leads to completely contradictory results at grazing incidence. A more rigorous solution is obtained, the procedure followed being exactly similar to that initiated by Sommerfeld to derive the electromagnetic field of a vertical dipole situated near a conducting plane. The results of such an analysis as applied to an acoustic point source are presented. As pointed out by Van Der Pol, the resultant solution may be regarded as that due to the point source and a diffuse image. The discussion of the solution is restricted to cases in which the sound source is at the boundary although it is given for all source heights. The solution shows that when the boundary medium has a high real specific acoustic impedance, non‐zero fields are obtained at all points along the boundary. For bounding media adequately described by ...

Attenuation and Dispersion of Elastic Waves in a Cylindrical Bar

The resonance method has been used to study the attenuation and dispersion of the first longitudinal mode of propagation and the dispersion of the first flexural mode of propagation of elastic waves in a cylindrical, aluminum alloy (24ST) rod. Q was found to decrease monotonically from 2.5×105 to 1.2×105 as the frequency increased from 0.84 to 100 kc. Longitudinal and flexural phase velocities are compared to Pochhammer‐Chree theory dispersion curves. Agreement of experimental and theoretical curves is within 0.3%. Similar agreement is obtained when normal flexural modes computed by a modified Timoshenko theory are compared to the experimental resonant frequencies. Measurements of torsional mode frequencies indicate dispersion does not exceed approximately 0.01% in the frequency range of approximately 0.5 to 100 kc.

On the Attenuation of Finite Amplitude Waves in a Liquid

An expression is obtained for the rate of attenuation of large amplitude waves of stable form propagated in a liquid whose attenuation varies as the square of the frequency. Calculations are presented for several liquids and comparison made with recent published data.

On the Attenuation of a Repeated Sawtooth Shock Wave

A formula which describes the space rate of change of amplitude of a repeated finite amplitude sawtooth wave is derived by application of the Rankine‐Hugoniot shock relations. Experimental evidence is in agreement as to the form of the amplitude change but gives lower rates of change than indicated by the formula.

Measurements of the Acoustic Radiation Pressure on a Sphere in a Standing Wave Field

A 1‐mm radius cork sphere was suspended by a fine vertical thread in a standing wave field whose axis of symmetry was horizontal. The force on the sphere was determined by the deflection from the vertical position. This force was determined as a function of axial position at a single frequency, and the dependence of the force, at a point halfway between the pressure node and antinode (the force is maximum at this point), on the acoustic amplitude was measured at several frequencies in the range 400 cps to 2800 cps. The maximum acoustic displacement amplitude used was less than the radius of the sphere but was of the same order of magnitude. The results are found to be in good quantitative agreement with the theory of L. V. King.

Surface and Volume Sources of Vorticity in Acoustic Fields

When a sound beam passes through a viscous fluid, vorticity is generated as a second‐order effect and streaming results. The work of Eckart, which considers the vorticity generated in the medium, is extended to consider “surface sources” of vorticity which appear when the sound beam makes contact with a solid, restraining surface. As in the Eckart work, the dynamic shear viscosity coefficient μ is assumed to be independent of the density changes which accompany a sound wave. However, the effect of a density dependent bulk viscosity coefficient is investigated, and it is found that the sources of vorticity are unaffected. Previous work on streaming by other authors is discussed and reconciled, and it is shown that in many cases the predominant sources of vorticity are the “surface sources.”

The Propagation of an Acoustic Wave Along an Absorbing Boundary

The sound field of a point source near a plane boundary (complex impedance) cannot be obtained by an acoustic ray approach. In fact such an approach, which utilizes the reflection coefficient for plane waves leads often to completely contradictory results. The procedure which must be followed is exactly similar to that initiated by Sommerfeld to derive the electromagnetic field of a vertical dipole situated near a conducting plane. The results of such an analysis as applied to an acoustic point source are presented. The solution forms the basis for the explanation of hitherto anomalous results. For convenience further discussion will be restricted to cases in which the sound source is at the boundary although the solution is given for all source heights. The solution shows that when the bounding medium has a high real specific acoustic impedance, non‐zero fields are obtained at all points along the boundary. For bounding media adequately described by simple porosity theory, the results are especially inte...

On the Attenuation of High Amplitude Waves of Stable Saw‐Tooth Form Propagated in Horns

The attenuation of high amplitude saw‐tooth waves of stable form in horns is investigated theoretically. The shock associated with each wave is assumed to be weak. An expression for the power loss for a generalized horn is obtained. Two quantities, the limiting particle velocity amplitude and the limiting power which is transmitted per refit throat area, occur in the solution. For long, gently tapering horns these are the limits to which the particle velocity and power tend as the input to the throat is increased. Uniform bore tubes, and exponential and conical horns, are discussed as particular examples of the general case.

Dispersion of Flexural Waves in a Cylindrical Bar

The first 260 flexural modes of a long (3‐m), thin (1.25‐cm) aluminum bar were measured. The frequency range covered was from 6 cycles to about 105 000 cycles. Comparison of the experimental dispersion curve is made with the Pochhammer‐Chree equations for an infinite bar. The dispersion curve is in reasonable agreement with the Pochhammer‐Chree theory. Normal modes computed by a modified Timoshenko theory for a finite bar are compared to the experimental resonant frequencies, and reasonable agreement is obtained.

Dispersion and Attenuation of Elastic Waves in a Cylindrical Bar

In the interests of determining the complex elastic constants of a given material (aluminum alloy) over a wide frequency range, the frequency and Q of a large multitude of overtones of a long (3‐m), thin (12‐in. diameter) bar were measured. These include the longitudinal mode and torsional mode. The frequency range covered was from about 0.5 kc to 100 kc. The elastic constants λ and μ are found to be relatively independent of frequency. The dispersion curve is in reasonable agreement with the Pochhammer‐Chree equations for an infinite bar. The Q of the longitudinal mode decreases from about 260 000 at the lowest frequency to 140 000 at the highest.