Frequency shifts for accelerated sources and observers: an illustration of non-locality in frequency measurement

Rothenstein, Bernhard; Sabata, Aldo De

doi:10.1088/0143-0807/19/6/010

Cited by 7 publications

(7 citation statements)

References 8 publications

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“…As a phenomenological alternative, a time-dependent frequency can also be defined as the inverse proper time between successive peaks [7][8][9][10]. This has the advantage of defining the frequency over an extended period of time, the same way it would be measured in practice.…”

Section: ͑11͒mentioning

confidence: 99%

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Nonlocal electrodynamics of linearly accelerated systems

Mashhoon

2004

Phys. Rev. A

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The measurement of an electromagnetic radiation field by a linearly accelerated observer is discussed. The nonlocality of this process is emphasized. The nonlocal theory of accelerated observers is briefly described and the consequences of this theory are illustrated using a concrete example involving the measurement of an incident pulse of radiation by an observer that experiences uniform acceleration during a limited interval of time.

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Section: ͑11͒mentioning

confidence: 99%

“…This frequency depends on the state of motion of the observer; therefore, equation (10) makes physical sense if the observer is able to measure the frequency ω ′ during a period of time in which v(t) does not change appreciably.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal electrodynamics of linearly accelerated systems

Mashhoon

2004

Phys. Rev. A

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“…The Doppler effect consists of a change in the frequency received by the receptor when the source moves relative to it, that is, the frequency increases when the receptor approaches the source and decreases when the receptor moves away from the source [1,2,3,4,5,6,7]. In our case, we have used a source at rest, and the receptor was moving.…”

Section: Introductionmentioning

confidence: 99%

The acoustic Doppler effect applied to the study of linear motions

2014

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Abstract. In this work, the change of frequency of a sound wave due to Doppler effect has been measured using a smartphone. For this purpose, a speaker at rest and a smartphone placed on a cart on an air track were used. The change in frequency was measured by using an application for Android TM "Frequency Analyzer"developed by us specifically for this work. This fact made possible the analysis of four types of mechanical motions: uniform linear motion, uniform accelerated linear motion, harmonic oscillations and damped harmonic oscillations. These experiments are suitable for undergraduate students. The main novelty of this work was the possibility of measuring the instantaneous frequency as a function of time with high precision. The results were compared with alternative measurements yielding a good agreement.

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“…Af ew theoretical attempts have been proposed to extend the theory of the Doppler effect to more complexgeometric and kinematic patterns compared to those which yield to the classical formula [9,10,11,12,13,14,15,16,17,18,19]. The validity of such treatments, which clarify different aspects of the phenomenon, is generally based on the correct predictions of particular cases for which analytical solutions are derived.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Correction to the Classical Doppler and Eco-Doppler Formulas

Biscarini¹,

Botti²,

Pettorossi³

2014

Acta Acustica united with Acustica

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The acoustic Doppler effect has been analytically investigated in the time domain for point source (S) and receiver (R) arbitrarily moving within a3Dhomogeneous and isotropic medium. Ageneral Doppler equation wasderived expanding the position vector of Si ns eries of powers of Δt at time t,a nd that of Ri ns eries of powers of Δt at time t ,a st he signal emitted by Sb etween the times t and t +Δtis receivedb yRb etween the times t and t +Δt .I nt he first-order approximation (retaining only terms of first-order in Δt and Δt ), this equation yields the classical Doppler and eco-Doppler formulas. In the second-order approximation (neglecting third and higher order terms in Δt and Δt ), the analytical solution of the equation wasd eriveda nd further expanded in series of powers to determine the analytical expression of the second-order correction factor to the classical Doppler and eco-Doppler formulas. This correction factor depends on both the transversal velocity and the longitudinal acceleration of S( at time t)a nd R( at time t ), with respect to the line direction joining the position of Sa t time t and that of Ra tt ime t .T he results indicate that the use of first-order approximation is fully justified in eco-Doppler ultrasound imaging, and highlight the conditions on the relevant physical parameters for which the second-order correction factor becomes considerable.

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Frequency shifts for accelerated sources and observers: an illustration of non-locality in frequency measurement

Cited by 7 publications

References 8 publications

Nonlocal electrodynamics of linearly accelerated systems

Nonlocal electrodynamics of linearly accelerated systems

The acoustic Doppler effect applied to the study of linear motions

Second-Order Correction to the Classical Doppler and Eco-Doppler Formulas

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