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An improved WKB calculation for a two-dimensional cochlear model

C R Steele, C E Miller

    The Journal of the Acoustical Society of America
    |July 1, 1980
    PubMed
    Summary
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    This study refines the WKB procedure for acoustic wave propagation, improving accuracy in the short wavelength region. Results show smooth variations in phase and damping along the cochlea, resolving previous irregularities.

    Area of Science:

    • Acoustics
    • Bioengineering
    • Mathematical Modeling

    Background:

    • Previous models like finite difference and WKB solutions showed discrepancies in the "phase plateau" region.
    • Irregularities in phase and damping functions were observed in short wavelength acoustic propagation.

    Purpose of the Study:

    • To improve the accuracy of the WKB procedure for analyzing acoustic wave propagation.
    • To investigate the behavior of phase and damping functions in the short wavelength region.
    • To achieve smoother variations in acoustic models along the cochlea.

    Main Methods:

    • Utilized a closed-form integral to enhance the WKB procedure.
    • Applied the improved WKB method to analyze acoustic wave propagation.
    • Focused on the short wavelength region for phase and damping function calculations.

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    Main Results:

    • The enhanced WKB procedure provides more accurate phase and damping functions.
    • Qualitative agreement was found with previous WKB and finite difference methods.
    • A smooth variation of acoustic properties with frequency and distance along the cochlea was observed.

    Conclusions:

    • The improved WKB procedure offers a more accurate and smoother model for acoustic wave propagation.
    • This advancement helps resolve irregularities previously seen in the "phase plateau" region.
    • The findings contribute to a better understanding of sound processing in the cochlea.