6/15/2023 0 Comments Koyal sound![]() In the case of a periodic distribution of scatterers, dissipation becomes a dominant factor that defines the efficiency of any acoustic device. Moreover, if the sound wave meets a set of solid boundaries, multiple reflections and viscous friction in narrow channels strongly increase energy losses. ![]() Velocity gradients within this viscous layer greatly exceed the gradients in the bulk, leading to much higher viscous losses than in free fluid. However, when a sound wave meets a solid boundary, a narrow viscous layer of thickness δ = ( 2 η / ( ω ρ ) ) 1 / 2 is formed. ![]() Therefore, viscous losses in the bulk can be neglected in the design of devices of sizes a few metres or centimetres. For frequencies around 100 kHz, the propagation length 1 / γ 0 of sound in water is several kilometres. For a monochromatic plane wave, the decay coefficient γ 0 = ω 2 ( 4 η / 3 + ξ ) / ( 2 ρ c 3 ) grows with frequency as ω 2, depending on the speed of sound c, and it is linear with respect to the viscosity coefficients η and ξ. In a homogeneous fluid of density ρ, the sound amplitude decays approximately as e − γ 0 x, where γ 0 is the decay coefficient. Dissipation accompanies propagation of sound in any elastic medium, leading to exponential decay of sound waves with distance.
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