Show that the crests of a wave = Asin(ax-bt) move tothe right at a speed equals

Question

Show that the crests of a wave = Asin(ax-bt) move tothe right at a speed equals the ratio of thecoefficients of t and x; that is, = b/a [Hint]: Focus attention on one wave crest P (for example, thecrest for which the argument of the sine function is/2) I am confused on this problem and really need some help.Thank you. Show that the crests of a wave = Asin(ax-bt) move tothe right at a speed equals the ratio of thecoefficients of t and x; that is, = b/a [Hint]: Focus attention on one wave crest P (for example, thecrest for which the argument of the sine function is/2) I am confused on this problem and really need some help.Thank you.

Explanation / Answer

    = Asin(ax-bt)    By comparing with progressive wave equation,y = A sin ( kx - t)    we get, propagation constant, k = aand angular frequency, = b                        But,k = 2 / and = 2f          Hence, = 2 / k   and f = /2    Wave velocity, V = f = ( /2 ) ( 2 / k ) = / k         Hence, V = b /a

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