# Study of Low-Frequency Hydroacoustic Waves' Behavior at the Shelf of Decreasing Depth
## 5 Analysis of the Results
If we compare this with the results of [3], obtained in the experiment with a low-frequency hydroacoustic emitter at 33 Hz, we can state that when the hydroacoustic emitter was operating at 22 Hz, much less energy went into the body waves than when the hydroacoustic emitter was operating at 33 Hz (78% [3]). From the theory of waveguide sound propagation, we can estimate the number of normal wave modes that emerge when a harmonic signal is emitted with frequency f for the waveguide depth h using the expression \(l<kh/\pi\), where \(k\) is the wave number and \(l\) is the number of mode of the normal wave. In this case, there is a condition for locking the waveguide \(kh<\pi\) (the waveguide depth is less than half the wavelength of the acoustic signal) under which only the zero mode can propagate. Thus, when the emitter is operating at 33 Hz at a depth of 30 m, two modes of normal waves should propagate--zero and first--while, when emitting 22 Hz at a depth of 32 m, only zero mode should propagate. We should note that with the effect of locking the waveguide and the propagation of several modes of normal waves, taking into account the principle of superposition, the pressure distribution across the waveguide remains the same. Moreover, high-order modes are inhomogeneous and quickly decay or transfer to other forms of energy, in contrast to the zero mode, which can propagate over long distances. Given all of the above, we can explain the large amount of hydroacoustic energy remaining in the water at 22 Hz emission by the effect of locking the waveguide, when only the zero mode appeared with concentrations of almost all the emitted energy in it. Whereas, in the experiment with the 33 Hz emitter, this effect did not occur, two modes were excited here. Subsequently, the energy from the first mode at a short distance from the emitter transferred into seismoacoustic energy in the form of body waves. The zero mode spread further along the water layer of the shelf with an energy equal to 22% of the energy generated by the emitter. As a result of the performed model calculations that were presented in the previous chapter of this article, a picture of the spatial distribution of hydroacoustic energy from the point of transmission was obtained and is shown in Figure 10.  
Figure 10 shows that the main portion of the energy generated by the hydroacoustic emitter is concentrated in water near it. Only a minor part of it goes to the bottom. While moving along the shelf of decreasing depth, the energy level decreases, which is associated with both cylindrical divergence and the transformation of hydroacoustic energy into seismoacoustic. In this case, the area of the highest concentration of hydroacoustic energy in the initial stage of its propagation from the emitter is at depths of 21-35 m. Moreover, careful examination of the figure shows that the horizontal energy level does not decrease monotonously, but changes \"quasi-periodically\", the scale of which is connected with the length of the hydroacoustic wave and is equal to 68 m. From the same figure, we can see that at depths slightly over 30 m, there is an abrupt decrease in hydroacoustic energy in the water, and it further drops at depths of about 16-17 m. The presence of energy in the water at shallower depths can only be explained by the undamped waves of the Rayleigh type leaking into the water. Figure 10: Spatial distribution of hydroacoustic energy from the transmitter to the coast along the receiving stations.