The equation describes a water wave moving in a straight line on a lake. y ( x , t ) = 3.75 cos ⁡ ( 0.450 x + 5.40 t )where y is the displacement perpendicular to the undisturbed surface of the lake. How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?

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The equation describes a water wave moving in a straight line on a lake.  y  (  x  ,  t  )  =  3.75  cos  ⁡  (  0.450  x  +  5.40  t  )where y is the displacement perpendicular to the undisturbed surface of the lake. How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?

Troncanizxl · Accepted Answer

On comparing the equation to   y  =  A  sin  ⁡  (  k  x  +  −  w  t  +  ϕ  ). We get   w  =  5.40      s          −      1      The time required for one complete wave to go part the fisherman, since the fisherman is at rest, is one time period.  T  =            2      π        w    =            2      ×      3.14        5.4    =  1.16     sA full wave takes 1.16 s to go past the fisherman.

The equation describes a water wave moving in a straight line on a lake. y...

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