a. Show that the Fourier component F(x)= Re[C exp(imx)] can be written as: F(x) |C| cos...

 

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a. Show that the Fourier component F(x)= Re[C exp(imx)] can be written as: F(x) |C| cos m (x+x) -1 = m- sin- (C/ |C) and C; stands for the imaginary part of C. where to b. In the study of atmospheric wave motions, it is often necessary to consider the possibility of amplifying or decaying waves. In such case we might assume that a solution has the form: Acos(kx vt kxo)exp(at) where A is the initial amplitude, a the amplification factor, and to the initial phase. Show that this expression can be written more concisely as: V = Re (Beik(x-ct)) = where both B and c are complex constants. Determine the real and imaginary parts of B and c in terms of A, a, k, v and xo. a. Show that the Fourier component F(x)= Re[C exp(imx)] can be written as: F(x) |C| cos m (x+x) -1 = m- sin- (C/ |C) and C; stands for the imaginary part of C. where to b. In the study of atmospheric wave motions, it is often necessary to consider the possibility of amplifying or decaying waves. In such case we might assume that a solution has the form: Acos(kx vt kxo)exp(at) where A is the initial amplitude, a the amplification factor, and to the initial phase. Show that this expression can be written more concisely as: V = Re (Beik(x-ct)) = where both B and c are complex constants. Determine the real and imaginary parts of B and c in terms of A, a, k, v and xo.

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The question refers to complex Fourier components and wave motions specifically in atmospheric science or similar physical contexts involving wave phe... View the full answer