450fall09hw10 - phase velocity expression is known to be v...

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ECE 450 Homework 10 Due: Tue, Nov 3, 2009, 5 PM 1. The propagation of ocean waves on the surface of deep water (depth much longer than a wavelength λ = 2 π k )isgovernedbythed ispers ionre lat ion ω = ± gk where g represents gravitational acceleration and ω , k are the frequency and wavenumber, respectively. a) Find the phase and group velocities v p = ω k and v g = ∂ω ∂k for deep water ocean waves. How are the two velocities related? b) If a rock falling into a calm, deep ocean, excites a continuous spectrum of waves with periods longer than T min seconds and shorter than T max seconds, where T max ± T min ,w i l lw a v e s oscillating with periods close to T min or
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Unformatted text preview: phase velocity expression is known to be v p = A √ ω , where A > is a real constant (which depends on density, radius, and Young’s modulus of the rod) and ω is the oscillation frequency in rad/s. a) Determine the unit for constant A in MKS system. b) Determine the group velocity expression for bending waves. c) Suppose on a very long rod a narrowband pulse of bending wave oscillations is excited, and the pulse is observed to travel on the rod from left to right. An observer moving to the right with the velocity of the pulse pays attention to the motion of the crests of the carrier of the pulse. Will he/she observe crest motions from right-to-left or from left-to-right? Explain clearly. 1...
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