The vertical displacement of an ocean wave is described by the function, y = A sin(ωt - kx). k is called the wave number (k = 2π/λ) and has a value of k = 18 rad/m. The remaining values are A = 9.5 m and ω = 14.5 rad/s.

a) Using y = A sin(B), input an expression for B where the wave would be traveling in the -x-direction. sig. gif?tid=7M79-31-9F-4E-8624-20536

b) What is the wave's velocity in m/s?

c) What is the wave's amplitude in m?

Explanation:

a ) y = A sin(B)  ; here B is the phase of the wave which moves so that it remains constant

ωt - kx = constant

differentiating on both sides

ωdt - kdx =0

ωdt =   kdx

dx / dt = ω / k

wave velocity = ω / k

b ) ω = 14.5 rad / s ,

k = 18 rad / m

wave velocity = ω / k

= 14.5 / 18

= .805 m /s

80.5 cm / s

c )

Amplitude = A

= 9.5 m

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