Peter J. Westervelt

Parametric Acoustic Array

This paper presents the theory of highly directional receivers and transmitters that may be “constructed” with the nonlinearity of the equations of fluid motion.

Acoustic Radiation Pressure

An expression obtained (1951) by the author for the radiation force on a scattering obstacle with arbitrary normal impedance is now shown to be valid for any scattering obstacle. The derivation of the final expression for the force in terms of the asymptotic scattering function for the obstacle in the field of an incident plane wave is accomplished by taking into account the interaction of the incident wave with the scattered wave. Thus the former assumption of a perfectly collimated beam (1951) is avoided by considering the incident plane wave to be of infinite extent. The result for the force in the direction of the incident wave is F∥ = c0−1{power scattered+power absorbed−∫Γs cosθdA} where c0 is the velocity of sound, Γs is the magnitude of the mean scattered intensity, θ is the angle formed between the incident and scattered waves. This is the same result as that obtained in 1951.The expression given in 1951 for the force perpendicular to the incident wave is correct only for an object which scatters ...

Laser‐excited broadside array

The expansions and contractions of an absorbing medium resulting from the passage of an intensity‐modulated laser are utilized to form a thermoacoustic array producing a highly directional acoustic wave propagating perpendicular to the axis of the laser beam.

The Mean Pressure and Velocity in a Plane Acoustic Wave in a Gas

The one‐dimensional wave equation is discussed to the second order of approximation by means of a transformation that carries the equation from the Eulerian to the Lagrangean form. Airys solution to this equation in Lagrangean form has been shown by Fubini to be an excellent approximation to an exact solution of Earnshaws equation of motion; therefore, Airys solution is chosen as the basis for much of this discussion. An expression for the local mean hydrostatic pressure in a plane progressive wave is obtained by transforming Airys solution from particle to local coordinates. In a similar way, the particle velocity in fixed coordinates is shown to possess a time‐independent component proportional to, and in a direction opposite to, the intensity vector This d.c. counter‐velocity is predicted without recourse to viscous forces and is compatible with zero average mass velocity. For a sound pressure level of 151 decibels in air there should exist a steady particle velocity of 1 cm/sec. Small particles su...

Parametric End‐Fire Array

A high‐power modulated sound beam acts like an end‐fire directional array for the modulation frequency. This occurs because the nonlinear terms in the equations of motion cause such a beam to act like a distribution of sources for the modulation frequency. If the sound beam is unmodulated, it behaves precisely like a parametric amplifier for any sound traveling in the direction of beam and thus can be used as a highly directional receiver. In order to test this concept, two carrier beams having approximately the same frequency ω1 ≈ ω2 ≈ ω were superposed on each other. The modulation frequency is then the difference ω8 = /ω1 − ω2/. If the pressure of each carrier is the same and equal to P0 the modulation percentage will be 100. The expression for the radiated intensity Is at a distance R0 far from this source is Is=ωs4P04S02[1 + 12ρ0c0−1(d2p/dρ2)]22(8π)2ρ03C09R02 × 1α2 + k2sin4(θ/2) in which S0 is the cross‐sectional area of the carrier beam, α is the pressure attenuation coefficient for the carrier beam...

Acoustic Radiation Force

A formula for the force on an arbitrary scatterer is derived without making any assumptions about the scatterer.

Absorption of sound by sound

Earlier studies [J. Acoust. Soc. Am. 29, 934 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other exhibited a singularity when the waves became collinear. The singularity is removed in this study, which leads to a method for calculating the pressure absorption coefficient α of a wave with wave vector k1 resulting from interaction with isotropic acoustic waves having the energy density spectrum u (k). Thus, α= (4ρ0c20)−1(1+1/2Λ)2π Fk1 0 ku (k) dk+k1F∞d1 2u (k) idk+k21Fk11k−1u (k) dk], in which ρ0 and c0 represent the density and velocity of sound of the fluid which is assumed to be dispersionless. The constant 1/2Λ =ρ0c d0−1(dc/dρ)ρ0.Subject Classification: [43]25.22, [43]25.35.

Effect of Sound Waves on Heat Transfer

A criterion recently derived by the author predicts the sound‐pressure level at which sound begins to increase the rate of heat transfer. The application of this criterion to recent experiments is discussed, and it is concluded that, while theory and experiment are in essential agreement, more experiments covering a wider range of variables are needed in order to test the full range of applicability of the theory.

Large‐Amplitude Pulse Propagation: A Transient Effect

The generation of transient signals by the propagation of large‐amplitude pulses has been investigated. Measurements of the transient signal along the axis of propagation of 10‐MHz pulses in carbon tetrachloride confirm the validity of the theoretical treatment of Berktay [J. Sound Vibration 2, 435–461 (1965)]. Data are also presented for the angular dependence of the transient signals generated by 20‐MHz pulses in water.

Large‐Amplitude Pulse Propagation—A Transient Effect. II

The generation of transient signals by the propagation of large‐amplitude pulses has been investigated. Measurements of the transient signal along the axis of propagation of 10‐MHz pulses in carbon tetrachloride confirm the validity of the theoretical treatment of Berktay [J. Sound Vibration 2, 435–461 (1965)]. Data are also presented for the angular dependence of the transient signals generated by 20‐MHz pulses in water.