3. The pressure, velocity and density perturbations for a one-dimensional acoustic wave are respectively given by p' = pei 。ik(x−ct), u' = ûeik(x-ct) and p' = peik(x−ct)¸ (a) Find the corresponding solutions for the zonal wind and density perturbations by relating û, ô to ô. These are known as polarization relations. [Hint: you may utilize the linearized equations of motion for u' and p' [in the notes or HH5 (5.20) and (5.21)], but you will have to linearize the nonlinear continuity equation [in the notes or HH5 (5.15)] to obtain an equation for p'. Note that û, rho and ô represent complex amplitudes, not unit vectors!] (b) In general, the complex amplitude ô can be written as p = |p|eis where p is the (real) amplitude and 6 is the (real) phase. Express the amplitude and phase for u' and p' in terms of the amplitude and phase of p'. For the fixed time t=0 sketch the variation of p', u', p' as a function of x for one wavelength. [HH 5.4]

3. The pressure, velocity and density perturbations for a one-dimensional acoustic wave are respectively given by p' = pei 。ik(x−ct), u' = ûeik(x-ct) and p' = peik(x−ct)¸ (a) Find the corresponding solutions for the zonal wind and density perturbations by relating û, ô to ô. These are known as polarization relations. [Hint: you may utilize the linearized equations of motion for u' and p' [in the notes or HH5 (5.20) and (5.21)], but you will have to linearize the nonlinear continuity equation [in the notes or HH5 (5.15)] to obtain an equation for p'. Note that û, rho and ô represent complex amplitudes, not unit vectors!] (b) In general, the complex amplitude ô can be written as p = |p|eis where p is the (real) amplitude and 6 is the (real) phase. Express the amplitude and phase for u' and p' in terms of the amplitude and phase of p'. For the fixed time t=0 sketch the variation of p', u', p' as a function of x for one wavelength. [HH 5.4]

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter35: Diffraction And Interference

Section: Chapter Questions

Problem 72PQ

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