A water wave traveling in a straight line on a lake is described by the equation.

$y (x, t) = 3.75 c m c o s (0.450 c m^{- 1} x + 5.40 s^{- 1} t)$

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?

1.16s

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3.48s

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2.32s

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4.64s

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Solution

The correct option is A 1.16s
on comparing the equation to

$y = A s i n (k x \pm ω t + ϕ)$

We get $ω = 5.40 s^{- 1}$

The time required for one complete wave to go part the fisherman, since the fisherman is at rest, is one time period.

$T = \frac{2 π}{ω} = \frac{2 \times 3.14}{5.4} = 1.16 s$

A full wave takes 1.16 s to go past the fisherman.

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The correct option is A 1.16son comparing the equation to y = A sin (kx± ωt+ϕ) We get ω = 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=2πω=2×3.145.4=1.16 s A full wave takes 1.16 s to go past the fisherman.