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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]

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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There is sketch in part B of this section please try to sketch the diagram. Show step by step how you reach for each section answer and also use letter used in this question it would be great

3. The pressure, velocity and density perturbations for a one-dimensional acoustic wave are respectively given by p' = peik(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 p. 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 p represent complex amplitudes, not unit vectors!] (b) In general, the complex amplitude ô can be written as p ples where p is the (real) amplitude and d 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] =
Transcribed Image Text:3. The pressure, velocity and density perturbations for a one-dimensional acoustic wave are respectively given by p' = peik(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 p. 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 p represent complex amplitudes, not unit vectors!] (b) In general, the complex amplitude ô can be written as p ples where p is the (real) amplitude and d 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] =
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