Wave theory modelling: a convenient approach to CW and pulse propagation modelling in low-frequency acoustics

1988 ◽  
Vol 13 (4) ◽  
pp. 186-197 ◽  
Author(s):  
F.B. Jensen
Keyword(s):  
Pulse Propagation ◽  
Low Frequency ◽  
Wave Theory ◽  
Convenient Approach ◽  
Propagation Modelling

scholarly journals Trapped Planetary (Rossby) Waves Observed in the Indian Ocean by Satellite Borne Altimeters

2017 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor
Keyword(s):  
Indian Ocean ◽  
Rossby Waves ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Theory ◽  
Planetary Waves ◽  
Sea Surface ◽  
Trapped Wave ◽  
The Indian Ocean ◽  
Frequency Variations

Abstract. Using 20 years of accurately calibrated, high resolution, observations of Sea Surface Height Anomalies (SSHA) by satellite ‎borne altimeters we show that in the Indian Ocean south of the Australian coast the low frequency variations of SSHA are ‎dominated by westward propagating, trapped, i.e. non-harmonic, planetary waves. Our results demonstrate that the ‎meridional-dependent amplitudes of the SSHA are large only within a few degrees of latitude next to the South-Australian ‎coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the ‎amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signals is analyzed by ‎employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely ‎between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The ‎estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of ‎harmonic Rossby (Planetary) waves by 140 % to 200 %. In contrast, the theory of trapped Rossby (Planetary) waves in a ‎domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase ‎speeds.‎

Investigations on Coherence of Active Control of Traffic Noise Transmission through an Open Window into a Rectangular Room in High-Rise Buildings

2003 ◽  
Vol 34 (8) ◽  
pp. 8-17
Author(s):  
Jiping Zhang
Keyword(s):  
Traffic Noise ◽  
Active Noise Control ◽  
Low Frequency ◽  
Wave Theory ◽  
High Rise ◽  
High Rise Building ◽  
Frequency Components ◽  
Open Window ◽  
Rectangular Room ◽  
Good Agreement

A method for theoretically calculating the coherence between sound pressure inside a rectangular room in a high-rise building and that outside the open window of the room is proposed. The traffic noise transmitted into a room is generally dominated by low-frequency components, to which active noise control (ANC) technology may find an application. However, good coherence between reference and error signals is essential for effective noise reduction and should be checked first. Based on traffic noise prediction methods, wave theory, and mode coupling theory, the results of this paper enable one to determine the potentials and limitations of ANC used to reduce such a transmission. Experimental coherence results are shown for two similar, empty rectangular rooms located on the 17th and 30th floors of a 34 floor high-rise building. The calculated results with the proposed method are generally in good agreement with the experimental results and demonstrate the usefulness of the method for predicting the coherence.

Numerical Simulation of Ultra-short Laser Pulses Propagation in Gas Media

2020 ◽  
Author(s):  
Katsiaryna Cidorkina ◽  
Alexander Svetashev ◽  
Ilya Bruchkouski ◽  
Siarhei Barodka ◽  
Leonid Turishev
Keyword(s):  
Numerical Simulation ◽  
High Power ◽  
Pulse Propagation ◽  
Stimulated Raman Scattering ◽  
Practical Interest ◽  
Wave Theory ◽  
Laser Pulses ◽  
Pure Nitrogen ◽  
Short Laser Pulses ◽  
Stimulated Raman

<p><span>Over the past ten years, important theoretical and practical results have been obtained in the field of interaction of high-power ultra-short laser pulses with solid transparent media. These results are significant for nonlinear optics and laser physics and are of practical interest for the development of femtosecond laser technology in sensing the environment, in the management of electrical discharge, in microphotonics.</span></p><p><span>However, many of the physical aspects of the supercontinuum generation and distribution of high-power femtosecond and attosecond laser pulses in an optically transparent gas media are not clear and require a detailed theoretical study.</span></p><p><span>Main objectives of the present study are the numerical simulation of high-intensity femtosecond pulses in the air, given the stimulated Raman scattering (SRS) and the stimulated Raman self-mode (SRSM) on pure nitrogen and oxygen molecules as well as on their mixtures.</span></p><p><span>Computer programs have been developed for solving nonlinear equations associated with the SRS and SRSM on the basis of a semi-classical energetic and wave theory with the help of numerical methods. </span></p><p><span>All calculations were made in the Visual Studio C ++ and Java programming environment. </span></p><p><span>The SRS mode for the distance of up to 5m for the main components of the air - nitrogen (78%) and oxygen (21%), in addition to the dynamics of the change of the pulse energy for different initial values have been calculated. </span></p><p><span>The propagation of SRMS laser pulses (λ=400, 800 nm; τ= 14, 20 fs) with positive chirp was numerically investigated for pulse energies 2π, π, π/100 and βz = 0.5, 1.0, 1.5.</span></p><p><span>The results obtained show that the dynamics of pulse propagation in SRMS mode is nonlinear in the pulse shape and spectrum. </span></p><p><span>It was estimated that the calculation results in energetic and wave models for </span>β<span>z≤1.5 are similar.</span></p>

Measurement of Vibration of the Basilar Membrane in the Squirrel Monkey

1974 ◽  
Vol 83 (5) ◽  
pp. 619-625 ◽  
Author(s):  
William S. Rhode
Keyword(s):  
Resonant Frequency ◽  
Squirrel Monkey ◽  
Basilar Membrane ◽  
Low Frequency ◽  
Wave Theory ◽  
Resonance Curve ◽  
Nerve Fibers ◽  
Neural Data ◽  
Oscillatory Response ◽  
Resonance Curves

The Mössbauer technique, which can be used to measure very small velocities, on the order of 0.2 mm/sec, has been used to measure the response of the basilar membrane to tones and clicks in squirrel monkeys. The results verify that there is a mechanical frequency analysis performed in the cochlea and that the traveling wave theory holds true. The resonance curves indicate that the tuning of the basilar membrane is greater than was thought. The basilar membrane in the 7–8 kHz region of the cochlea vibrates nonlinearly at frequencies near the “resonant frequency.” The click response shows that the “tail” of the decaying oscillatory response does not decrease in proportion to click amplitude while the early displacements of the basilar membrane have a nearly linear relationship with click amplitude. These results are in good agreement with the results of the measurements using tones as stimuli. Experiments examining postmortem behavior of the basilar membrane indicate a rapid decrease in the sensitivity of vibration along with a decrease of up to one octave in the “resonant” frequency within a six hour period after the animal's death. The shift in resonant frequency is accompanied by a corresponding shift in the phase characteristic. The low frequency slope of the resonance curve becomes 6 dB/octave exactly as Békésy found while the high frequency slope decreases slightly. Comparison of the mechanical resonance curves with the neural data for single auditory nerve fibers in the squirrel monkey indicates that the exquisite tuning exhibited in the nerve cannot be explained solely on the basis of the mechanical behavior of the basilar membrane.

scholarly journals Trapped planetary (Rossby) waves observed in the Indian Ocean by satellite borne altimeters

Ocean Science ◽  
2017 ◽  
Vol 13 (3) ◽  
pp. 483-494 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor
Keyword(s):  
Indian Ocean ◽  
Rossby Waves ◽  
Low Frequency ◽  
Propagation Speed ◽  
Wave Theory ◽  
Planetary Waves ◽  
Sea Surface ◽  
Trapped Wave ◽  
The Indian Ocean ◽  
Frequency Variations

Abstract. Using 20 years of accurately calibrated, high-resolution observations of sea surface height anomalies (SSHAs) by satellite borne altimeters, we show that in the Indian Ocean south of the Australian coast the low-frequency variations of SSHAs are dominated by westward propagating, trapped, i.e., non-harmonic, Rossby (Planetary) waves. Our results demonstrate that the meridional-dependent amplitudes of the SSHAs are large only within a few degrees of latitude next to the southern Australian coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signal is analyzed by employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of harmonic Rossby (planetary) waves by 140 to 200 % (which was also reported in previous studies). In contrast, the theory of trapped Rossby (planetary) waves in a domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase speeds in the study area.

A Note on the Second-Order Contribution to Extreme Waves Generated During Hurricanes

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Mark L. McAllister ◽  
Thomas A. A. Adcock ◽  
Paul H. Taylor ◽  
Ton S. van den Bremer
Keyword(s):  
Wind Waves ◽  
Low Frequency ◽  
Nonlinear Behavior ◽  
Wave Theory ◽  
Linear Range ◽  
Second Order ◽  
Linear Wave ◽  
Extreme Waves ◽  
Order Difference ◽  
Hurricane Wind

High wind speeds generated during hurricanes result in the formation of extreme waves. Extreme waves by nature are steep meaning that linear wave theory alone is insufficient in understanding and predicting their occurrence. The complex, highly transient nature of the direction of wind and hence of waves generated during hurricanes affects this nonlinear behavior. Herein, we examine how this directionality can affect the second-order nonlinearity of extreme waves generated during hurricanes. This is achieved through both deterministic calculations and experiments based on the observations of Young (2006, “Directional Spectra of Hurricane Wind Waves,” J. Geophys. Res. Oceans, 111(C8), epub). Our calculations show that interactions between the tail and peak of the spectrum can become significant when they travel in different directions, resulting in second-order difference components that exist in the linear range of frequencies. These calculations are generally supported by experimental observations, but we note the difficulty of generating and focusing the high-frequency tail of the spectrum experimentally. Bound second-order difference components or subharmonics typically exist as low frequency infra-gravity waves. Components that exist in the linear range of frequencies may be missed by conventional methods of processing field data where low-pass filtering is used and hence overlooked. In this note, we show that in idealized directional spreading conditions representative of a hurricane, failing to account for second-order difference components may lead to underestimation of extreme wave height.

The finite-product method in the theory of waves and stability

2009 ◽  
Vol 466 (2114) ◽  
pp. 471-491 ◽  
Author(s):  
C. J. Chapman ◽  
S. V. Sorokin
Keyword(s):  
Dispersion Relation ◽  
Elastic Waves ◽  
Low Frequency ◽  
Wave Theory ◽  
Finite Product ◽  
High Frequencies ◽  
Polynomial Approximations ◽  
Wide Range ◽  
Product Method ◽  
Finite Products

This paper presents a method of analysing the dispersion relation and field shape of any type of wave field for which the dispersion relation is transcendental. The method involves replacing each transcendental term in the dispersion relation by a finite-product polynomial. The finite products chosen must be consistent with the low-frequency, low-wavenumber limit; but the method is nevertheless accurate up to high frequencies and high wavenumbers. Full details of the method are presented for a non-trivial example, that of anti-symmetric elastic waves in a layer; the method gives a sequence of polynomial approximations to the dispersion relation of extraordinary accuracy over an enormous range of frequencies and wavenumbers. It is proved that the method is accurate because certain gamma-function expressions, which occur as ratios of transcendental terms to finite products, largely cancel out, nullifying Runge’s phenomenon. The polynomial approximations, which are unrelated to Taylor series, introduce no spurious branches into the dispersion relation, and are ideal for numerical computation. The method is potentially useful for a very wide range of problems in wave theory and stability theory.

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