Nonlinear propagation of spherically diverging high‐intensity jet noise

High intensity focused ultrasound (HIFU) is a noninvasive medical procedure during which a large amount of energy is deposited in a short duration which causes sudden localized rise in tissue temperature, and ultimately, cell necrosis. In assessing the influence of HIFU on biological tissue, semi-empirical mathematical models can be useful for predicting thermal effects. These models require values of the pressure amplitude in the tissue of interest, which can be difficult to obtain experimentally. One common method for estimating the pressure amplitude in tissue is to operate the HIFU transducer in water, measure the pressure amplitude, then multiply by a scaling factor that accounts for the difference in attenuation between water and tissue. This procedure can be accurate when the ultrasound amplitude is low, and the pressure trace in tissue is proportional to that in water. Because of this proportionality, the procedure for reducing the amplitude from water to tissue is called linear derating. At higher intensities, however, harmonics of the fundamental frequency are generated due to nonlinear propagation effects. Higher harmonics are attenuated differently in water and tissue (Hamilton and Blackstock [1]), and the pressure waves in water and tissue are no longer proportional to one another. Techniques for nonlinearly transforming pressure amplitudes measured in water to values appropriate for tissue are therefore desirable when bioeffects of higher intensity procedures are being studied. These techniques are labeled “nonlinear derating”.

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‘Crackle’: an annoying component of jet noise

Journal of Fluid Mechanics ◽

10.1017/s0022112075002558 ◽

1975 ◽

Vol 71 (2) ◽

pp. 251-271 ◽

Cited By ~ 120

Author(s):

J. E. Ffowcs Williams ◽

J. Simson ◽

V. J. Virchis

Keyword(s):

High Speed ◽

Angular Position ◽

Jet Noise ◽

Wide Frequency Range ◽

Nonlinear Propagation ◽

Wave Form ◽

Long Term Effects ◽

Recorded Sound ◽

Recording Process

The paper describes an investigation of a subjectively distinguishable element of high speed jet noise known as ‘crackle’. ‘Crackle’ cannot be characterized by the normal spectral description of noise. It is shown to be due to intense spasmodic short-duration compressive elements of the wave form. These elements have low energy spread over a wide frequency range. The crackling of a large jet engine is caused by groups of sharp compressions in association with gradual expansions. The groups occur at random and persist for some 10−1s, each group containing about 10 compressions, typically of strength 5 × 10−3 atmos at a distance of 50 m. The skewness of the amplitude probability distribution of the recorded sound quantifies crackle, though the recording process probably changes the skewness level. Skewness values in excess of unity have been measured; noises with skewness less than 0·3 seem to be crackle free. Crackle is uninfluenced by the jet scale, but varies strongly with jet velocity and angular position. The jet temperature does not affect crackle, neither does combustion. Supersonic jets crackle strongly whether or not they are ideally expanded through convergent-divergent nozzles. Crackle is formed (we think) because of local shock formation due to nonlinear wave steepening at the source and not from long-term nonlinear propagation. Such long-term effects are important in flight, where they are additive. Some jet noise suppressors inhibit crackle.

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