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?

Question

Physics

Halle

4 August, 11:39

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?

+4

Answers (1)

Know the Answer?

Naima Burton · Answer 1

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