Interaction of sound waves. Part I: Basic equations and plane waves

1987 ◽  
Vol 82 (4) ◽  
pp. 1425-1428 ◽  
Author(s):  
Jacqueline Naze Tjo/tta ◽  
Sigve Tjo/tta
Keyword(s):  
Plane Waves ◽  
Sound Waves ◽  
Basic Equations

Sound Propagation in Dilute Polyatomic Gases

1972 ◽  
Vol 27 (4) ◽  
pp. 583-592
Author(s):  
H. Moraal ◽  
F. Mccourt
Keyword(s):  
Pressure Range ◽  
Sound Propagation ◽  
Plane Waves ◽  
Point Of View ◽  
Perturbation Function ◽  
Sound Waves ◽  
Polyatomic Gas ◽  
Measured Pressure ◽  
Theory And Experiment ◽  
Good Agreement

Abstract Sound propagation in dilute pure gases, both monatomic and polyatomic, has been considered from the point of view of the Waldmann-Snider equation. It is shown that the commonly employed assumption that sound propagation in gases is equivalent to the propagation of plane waves is valid only in the region where collisions restore equilibrium faster than it is perturbed by the sound waves. A systematic truncation procedure for an expansion of the perturbation function in irreducible Cartesian tensors is introduced and then illustrated in solutions for three specific kinds of molecules, helium, nitrogen and rough spheres. The agreement between theory and experiment is rather good for sound absorption in the region where the ratio of the collision and sound frequencies is greater than 1.5. The agreement in the case of dispersion is good over the whole measured pressure range. One useful result obtained is to show the polyatomic gas calculations in second approximation have as good agreement with experiment as the calculations for noble gases in third approximation. This can be related to the possession by the polyatomic gas of a bulk viscosity which dominates in sound propagation.

scholarly journals On the acoustic disturbances produced by small bodies in plane waves transmitted through water, with special reference to the single-plate direction finder

1921 ◽  
Vol 100 (704) ◽  
pp. 261-288
Keyword(s):  
Special Reference ◽  
Plane Waves ◽  
Maximum Amplitude ◽  
Sound Waves ◽  
Small Bodies ◽  
Acoustic Disturbances ◽  
Sense Of Direction ◽  
Single Plate ◽  
Direction Finder ◽  
Metal Diaphragm

The experiments to be described were carried out for the Board of Invention and Research, under the direction of Sir William Bragg, between October 1916 and February 1917, on the Cullaloe Reservoir, near Aberdour, Fifeshire, and are now published with the permission of the Admiralty. A form of directional hydrophone has already been described by Sir William Bragg. It consists of a metal diaphragm, A, about four inches in diameter, mounted in a heavy ring, B, and open to the water on both sides ( vide Chart 9). In the centre of the diaphragm is a small metal box, C, carrying a carbon granule microphone of the button type. The microphone is connected into an ordinary telephone circuit. If the instrument is rotated about a vertical diameter in water through which sound waves are passing the sound heard in the receivers passes through a number of maxima and minima. When the diaphragm is turned “edge-on” to the source of sound it is obvious that the pressure pulses will reach the two faces of the diaphragm symmetrically and the diaphragm will fail to vibrate. As, however, either face is turned toward the source this symmetry ceases to exist and the diaphragm is thrown into vibration, which reaches a maximum amplitude when the instrument is “broad-side” on to the source. The instrument, therefore, indicates the line of propagation of the sound, but owing to the existence of two positions of maximum or minimum its indications are ambiguous as regards the sense of direction.

scholarly journals Developments in the Reflection of plane waves

2021 ◽  
Vol 23 (07) ◽  
pp. 950-956
Author(s):  
Surbhi Sharma ◽  
◽  
Heena Sharma ◽  
Keyword(s):  
Free Surface ◽  
Initial Stress ◽  
Plane Waves ◽  
Elastic Media ◽  
Basic Equations ◽  
Hydrostatic Initial Stress

The present paper deals with the reflection of plane waves from the free surface. In this paper, we discuss the relatable background of the reflection of plane waves. The basic equations for isotropic and homogeneous generalized thermo-elastic media under hydrostatic initial stress are discussed in the context of thermo-elasticity.

Used in Acoustic Projects Calculation of Reflection Coefficient for End Opening of Channel without Flange

2017 ◽  
Vol 6 (3) ◽  
pp. 34-41
Author(s):  
Владимир Тупов ◽  
Vladimir Tupov ◽  
А. Миронова ◽  
A. Mironova
Keyword(s):  
Reflection Coefficient ◽  
Error Analysis ◽  
Plane Waves ◽  
Computational Error ◽  
Sound Waves ◽  
Computer Approach ◽  
Coefficient Of Reflection ◽  
Plane Sound ◽  
Opening Channel

The computational error analysis for coefficient of reflection of plane sound waves at the end of opening channel without flange performed by means of formulas commonly used in practice has demonstrated their unacceptability for accurate acoustic calculations, and limitations of the Helmholtz numbers’ range, where these formulas are applicable. In this work have been proposed calculated dependences, convenient for practical usage and enabling more accurately calculate by computer approach the considered quantity’s values in a whole range of existence of the plane waves in the channel.

BEHAVIOR OF SOUND WAVES IN SHEPHERD FLUTE ON THE BASIS OF QUANTUM THEORY OF INDIVIDUAL PHONONS

2010 ◽  
Vol 24 (17) ◽  
pp. 3439-3452
Author(s):  
SONJA KRSTIĆ ◽  
VJEKOSLAV SAJFERT ◽  
BRATISLAV TOŠIĆ
Keyword(s):  
Quantum Theory ◽  
Hyperbolic Equation ◽  
Plane Waves ◽  
Sound Waves ◽  
High Frequencies ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation ◽  
Theory And Experiment ◽  
Good Agreement

Using the linearized Hamiltonian of individual phonon, it was shown that Schrödinger's equation of individual phonon is by form identical with classical hyperbolic equation. It was also shown that damper in shepherd's flute is reflexive for high frequencies and transparent for low ones. This result was experimentally tested by authors and good agreement of theory and experiment was found. The propagation of sound in parallelopipedal and cylindrical shepherd's flute was investigated. It turned out that parallelopipedal sound propagates in z-direction, only, while in cylindrical one besides plane waves in z-direction the damped waves in x, y plane appear.

Ultrasound Beam Radiated From Circular Piston in Bubbly Liquids: Nonlinear Analysis for Envelope of Short Waves With Diffraction Effect

2011 ◽  
Author(s):  
Junya Kawahara ◽  
Tetsuya Kanagawa ◽  
Takeru Yano ◽  
Kazumichi Kobayashi ◽  
Masao Watanabe ◽  
...  
Keyword(s):  
Fluid Model ◽  
Plane Waves ◽  
Bubbly Liquid ◽  
Physical Parameters ◽  
Diffraction Effect ◽  
Bubble Wall ◽  
State Equations ◽  
Dinger Equation ◽  
Ultrasound Beam ◽  
Basic Equations

A weakly diffracted ultrasound beam radiated from a circular piston placed in a bubbly liquid is formulated in terms of a wave equation based on scaling relations of physical parameters [1]: typical propagation speed, period, wavelength, and diameter of beam. We derive a nonlinear evolution equation for the modulation of quasi-monochromatic waves for the case of a short wavelength with a moderately high frequency from a set of basic equations for bubbly flows: conservation equations of mass and momentum for gas and liquid in a two-fluid model, Keller’s equation for bubble wall motion, state equations for gas and liquid, and so on. The compressibility of liquid is taken into account, and thus the waves are attenuated due to bubble oscillations. The viscosity of gas, heat conduction in gas and liquid, and phase change across bubble wall are ignored. As a result, the nonlinear Schro¨dinger equation for the envelope of the beam with diffraction effect is derived from the basic equations. For plane waves the diffraction term does not appear, and hence our equation is reduced to the original nonlinear Schro¨dinger equation [1].

scholarly journals Measurement of absorbing power of materials by the stationary wave method

1930 ◽  
Vol 127 (804) ◽  
pp. 89-110 ◽  
Keyword(s):  
Plane Waves ◽  
Stationary Wave ◽  
Small Samples ◽  
Wave System ◽  
Pressure Amplitude ◽  
Wave Method ◽  
Sound Waves ◽  
Reflected Waves ◽  
Velocity Amplitude ◽  
The Difference

The stationary wave method of determining the absorption coefficient of a material employs plane waves of sound at perpendicular incidence. It requires the use of only small samples of material and provides a rapid and convenient means of obtaining useful information. The principle of the method has been previously described, so that a brief outline is sufficient. A long pipe is provided with a source of sound at one end and is closed at the other by the test specimen. Sound waves from the source travel down the pipe and are reflected by the specimen to an extent depending on its absorbing power. The superposition of the incident and reflected waves gives rise to a stationary wave system, and the pressure amplitude varies continuously along the pipe, going through a series of maximum and minimum values. The same description applies to the velocity amplitude, with the difference that the pressure maxima coincide in position with the velocity minima and vice versa .

A new approach to problems of shock dynamics Part I Two-dimensional problems

1957 ◽  
Vol 2 (2) ◽  
pp. 145-171 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Wave Propagation ◽  
Mach Number ◽  
Mach Reflection ◽  
Linear Equations ◽  
Plane Waves ◽  
Propagation Speed ◽  
Approximate Theory ◽  
Two Dimensional ◽  
Sound Waves ◽  
Mathematical Techniques

In this paper, two-dimensional problems of the diffraction and stability of shock waves are investigated using an approximate theory in which disturbances to the flow are treated as a wave propagation on the shocks. These waves carry changes in the slope and the Mach number of the shock. The equations governing the wave propagation are analogous in every way to the non-linear equations for plane waves in gas dynamics, and their solutions can be deduced by the same mathematical techniques. Since the propagation speed of the waves is found to be an increasing function of Mach number, waves carrying an increase in Mach number will eventually break and form what we may call a ‘shock’, corresponding to the breaking of a compression wave into a shock in the ordinary plane wave case. Such a ‘shock’ moving on the shock is called ashock-shock.The shock-shock is a discontinuity in Mach number and shock slope, and it must be fitted in to satisfy the appropriate relations between these are interpreted as the trace of cylindrical sound waves in the flow behind the shock. In particular a shock-shock is the trace of a genuine shock in the flow behind, and thus corresponds to Mach reflection.The general theory of the wave propagation is set out in § 2. The subsequent sections contain applications of the theory to specific problems, including the motion of a shock along a curved wall, diffraction by a wedge, stability of plane shocks and the instability of a converging cylindrical shock.

scholarly journals Scanning Acoustical Microscopy

1994 ◽  
Vol 2 (5) ◽  
pp. 26-28
Author(s):  
Jacqueline Gailet
Keyword(s):  
High Frequency ◽  
Plane Waves ◽  
Sound Waves ◽  
Spherical Lens ◽  
Biomedical Analysis ◽  
Physical Laws ◽  
The Waves ◽  
Non Destructive ◽  
Scanning Acoustic Microscope ◽  
High Sound

One of Olympus' not well known product in the American market is the UH3 Scanning Acoustic Microscope (SAM). This state of the art, highly versatile microscope has many applications from non-destructive imaging to biomedical analysis, to pharmaceutical applications to name a few areas of current industrial interest.The principle behind SAM is quite simple, and uses the basic physical laws of reflection. High frequency sound waves are mechanically produced by a piezoelectric crystal. A high voltage impulse spike starts the crystal vibrating at its preset resonant frequency emitting acoustical plane waves through a medium with a relatively high sound velocity such as sapphire. The waves are made to converge by a half-spherical lens at the bottom of the sapphire rod. The diameter of the lens is less than one millimeter and depends on the operating frequency. The lower the frequency, the larger is the diameter of the lens.

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