Consider sound waves propagating in an atmosphere with a horizontal wind. Assume that the sound speed C,
Question:
Consider sound waves propagating in an atmosphere with a horizontal wind. Assume that the sound speed C, as measured in the air’s local rest frame, is constant. Let the wind velocity u = uxex increase linearly with height z above the ground: ux = Sz, where S is the constant shearing rate. Consider only rays in the x-z plane.
(a) Give an expression for the dispersion relation ω = Ω(x, t ; k).
(b) Show that kx is constant along a ray path, and then demonstrate that sound waves will not propagate when
(c) Consider sound rays generated on the ground that make an angle θ to the horizontal initially. Derive the equations describing the rays, and use them to sketch the rays, distinguishing values of θ both less than and greater than π/2.
Step by Step Answer:
Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics
ISBN: 9780691159027
1st Edition
Authors: Kip S. Thorne, Roger D. Blandford