Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 116

For a homogeneous plane sound wave at normal incidence on a fluid medium of different characteristic impedance ρc, both reflected and transmitted waves are formed (see Figure 3.13).

Figure 3.13 Incident intensity I_i, reflected intensity I_r, and transmitted intensity I_t in a homogeneous plane sound wave at normal incidence on a plane boundary between two fluid media of different characteristic impedances.

From energy considerations (provided no losses occur at the boundary) the sum of the reflected intensity I_r and transmitted intensity I_t equals the incident intensity I_i:

(3.64)

and dividing throughout by I_i,

(3.65)

where R is the energy reflection coefficient and T is the transmission coefficient. For plane waves at normal incidence on a plane boundary between two fluids (see Figure 3.13):

(3.66)

and

(3.67)

Some interesting facts can be deduced from Eqs. (3.66) and (3.67). Both the reflection and transmission coefficients are independent of the direction of the wave since interchanging ρ₁ c₁ and ρ₂ c₂ does not affect the values of R and T. For example, for sound waves traveling from air to water or water to air, almost complete reflection occurs, independent of direction; the reflection coefficients are the same and the transmission coefficients are the same for the two different directions.