Question

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y( x, t) = 3.7 cos(2.2 x - 5.6 t), where all quantities are in SI units.

Answer 1

Answer:

$\frac{\partial y(x,t)}{\partial t} = 20.72\cdot \sin(2.2\cdot x-5.6\cdot t)$

Step-by-step explanation:

The vertical speed of an ocean wave at any point and any time is obtained by using partial derivatives in the vertical displacement function. That is to say:

$\frac{\partial y(x,t)}{\partial t} = -3.7\cdot \sin(2.2\cdot x - 5.6\cdot t)\cdot (-5.6)$

$\frac{\partial y(x,t)}{\partial t} = 20.72\cdot \sin(2.2\cdot x-5.6\cdot t)$