Some Properties of Longitudinal Shear Waves: A Study by Computer Simulation
Shyam M. Khanna, Richard E. Sears, Juergen Tonndorf · The Journal of the Acoustical Society of America · 1968
Shearing between the basilar membrane and tectorial membrane is known to contribute towards mechanical processing of the auditory signals. The amplitude of the longitudinal shear wave has been given by von Békésy to be proportional to the vertical amplitudes of the basilar membrane and the first space derivative of the momentary position of the traveling wave along the basilar membrane. Traveling waves were generated on a digital computer using a modified form of Flanagan's mathematical model. Shear waves were obtained from these by taking the first instantaneous space derivatives. Envelopes for the longitudinal shear vibrations are compared to those of the traveling waves. These comparisons show that: (1) The maxima of the shear wave envelopes are slightly closer to the helicotrema. (2) The shear waves are much more localized along the basilar membrane. (3) Localization is much more pronounced at low frequencies than the equivalent entities of the traveling wave. Comparisons made between the resonance curves of traveling-wave vibrations and shear-wave vibrations show considerable sharpening of the shear-wave envelopes towards the low frequencies. The effect of middle ear transmission on the resonance curves is shown.