Thermoviscous Attenuation of Plane, Periodic, Finite‐Amplitude Sound Waves

摘要: The propagation of a plane progressive wave finite amplitude in thermoviscous fluid is considered. taken to be purely sinusoidal shape at its source. approach through Burgers equation, which very good approximation the exact equations motion when effects nonlinearity and dissipation are relatively small but definitely not negligible. A complicated solution Burgers' equation analyzed. nature found depend strongly on parameter Γ, represents importance relative dissipation. Nonlinear prove significant Γ>1, finding agreement with criterion proposed by Gol'dberg (Akust. Zh. 2, 325 (1956) [English transl.: Soviet Phys.—Acoust. 346(1956)]) concerning appearance shock waves. When Γ>>1, simple asymptotic representations terms Fourier series may obtained. One these corresponds Fay's [J. Acoust. Soc. Am. 3, 222 (1931)]. An equivalent “time‐domain” representation shows clearly sawtooth behavior wave. region extend approximately point x=O.6/α, where α dimensional small‐signal attenuation coefficient. Curves extra suffered fundamental as result nonlinear given for values Γ range 1–100 000. If large, decibels approaches value −12+20 log10Γ distance from source becomes large. 1 dB below asymptote attained x=1/α. Application waves argon air discussed. It that employed increase efficiency long‐range sound transmission. possible application low‐frequency ocean also