as gh Surfer\'s Speed Problem This problem addresses the interesting phenomena i
ID: 2270582 • Letter: A
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Surfer's Speed Problem This problem addresses the interesting phenomena in which an object that moves on a wave, like a surfer, can have a speed greater than the wave speed. Some people have suggested this as a way to travel faster than light. A surfer is riding a traveling water wave that is moving towards the shore. The crest of the wave forms a line that is approximately parallel to the shoreline. The surfer rides on top of the crest. This crest moves towards the shoreline at a speed of about 6.1 m/s. Surprisingly, however, the magnitude of the velocity of the surfer as measured by an observer on the shoreline is not 6.1 m/s, but. 6.7 m/s. Explain why the speed of the surfer can be greater than the speed of the wave. What is the direction of the surfer's velocity vector as expressed as an angle between the velocity vector and a line perpendicular to the shoreline? Is the surfer's velocity vector perpendicular to the shoreline, parallel to the shoreline or somewhere in between? If the surfer's velocity vector is neither perpendicular to the shoreline nor parallel to the shoreline break find the component of the surfer's velocity vector that is perpendicular to the shoreline and the component that is parallel to the shoreline. Where does the parallel component come from? Solutions to the Wave Equation Problem We write down the wave equation as Show that y(x, t) = ym sin {kx - wt) satisfies this equation by direct differentiation. Show that y(x,t) = h {kx - wf ) also satisfies the wave equation, where h represents any function at all. Wave Velocity Problem Consider a sinusoidal wave y(ar,t) = r/m sin (kx - ut). Consider points on the wave of constant phase and the definitions of wavelength, A and frequency, f. to obtain an expression for wave speed in terms of A and f.Explanation / Answer
as gh Surfer's Speed Problem This problem addresses the interesting phenomena i
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