The article is devoted to the analysis of the vertical structure of the acoustic pressure field and the first-mode particle velocity in a hydroacoustic waveguide in shallow water. A waveguide consisting of a water layer with a constant sound velocity profile, a transition layer, and a half-space is considered. The acoustic properties of the transition layer are assumed to be frequency dependent. Formulas are derived that describe the vertical profile of the normal mode of a particle velocity. The transformation of the vertical profile of the first mode with increasing frequency is analyzed. The phase difference relations between the normal mode of acoustic pressure and particle velocity are analyzed. A relationship is established between the change in the vertical structure of the normal modes of pressure and particle velocity and the acoustic properties of the transition layer.

Keywords: normal modes, particle velocity, seabed, attenuation coefficient

The article considered the propagation of a long impulse signal in a hydroacoustic waveguide. A solution is given for a replica of a impulse signal in the second approximation of the dispersion theory. The propagation of a single-mode and multimode impulse in a Pekeris waveguide with a bottom in the form of an absorbing half-space is simulated. The acoustic properties of the half-space correspond to medium sand with an average grain size 0,3 mm. The result of the solution in the second approximation of the dispersion theory is compared with the result of the simulation of the impulse replica obtained as a convolution of the input signal with the impulse response of the waveguide. The disadvantages of the solution in the second approximation of the dispersion theory are shown and analyzed. It is shown that the theory of dispersion incorrectly reproduces the transients when the signal is switched on and off in cases where the signal frequency lies near the critical frequency of the first or second mode. It is shown that the theory of dispersion correctly reproduces the envelope of a multimode impulse signal.

Keywords: impulse signal, normal modes, group velocity, dispersion theory, intramode dispersion, intermode dispersion

A hydroacoustic waveguide is considered as a linear system with parameters distributed over dis-tance. A method is proposed for modeling the impulse response of a waveguide. The fields of indi-vidual normal modes at fixed frequencies are calculated so that discretization theorems are satisfied. By performing the inverse Fourier transform of the fields of all modes separately, the time realiza-tions are restored. Then, summing the mode fields, the impulse response of the waveguide is calcu-lated. This approach allows you to "turn off" the fields of individual modes, add, if necessary, the fields of higher modes, or to study all fields separately, simulating the operation of mode selection. The impulse response is considered as a tool for solving the problems of inverting the acoustic characteristics of the seabed and modeling the propagation of signals in waveguides. The impulse response of the first mode of the Pekeris waveguide with the bottom in the form of an intermediate layer and half-space is restored, its wave attributes are revealed: ground wave, water wave, Airy wave. The frequency dependences of the group velocity of normal modes and the multimode im-pulse response are restored. Low-pass filtering of the impulse response makes it possible to reveal the Airy phase of the first mode.

Keywords: normal modes, seabed, attenuation coefficient, group velocity, impulse response, intramode dispersion, intermode dispersion