The pressure

Where

In this simplified calculation, we assume that there are only two types of losses: the first, associated with the absorption of sound in the medium, described by the absorption coefficient

The second type of loss is associated with the geometric spreading of the signal energy and is described as follows:

where

The total path loss can now be described as follows:

A factor of 0.001 is used to convert dB/km to dB/m.

Now we can write the equation from which we define

Or, substituting (3) into (4):

Obviously,

Equation (5) in its general form cannot be solved analytically, and the use of numerical methods is required. In this document, Newton's method is used.

Parameter | Notation | Value | Range | Units | Description |
---|---|---|---|---|---|

Maximal distance | r_{max} |
m | |||

Number of iterations taken | N_{i} |
1 .. 1000 | |||

Residual | ε |
m |

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