Question

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?

Answer 1

Answer:

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

Answer 2

The velocity of the wave is 0.805 m/s and the amplitude of the wave is 9.5 m/s.

a ) The vertical displacement of an ocean wave,

y = A sin(B)

Where,

B - phase of the wave which moves so it remain constant  

ωt - kx = constant  

Differentiate on the both sides  

ωdt - kdx =0  

ωdt =   kdx  

$\bold {\dfrac {dx} {dt }= \dfrac {\omega }{ k}}$  

So, velocity of the wave = ω / k  

b ) The velocity of the wave,

$\bold {\omega }$= 14.5 rad / s ,  

k = 18 rad / m  

$\bold {v = \dfrac w{k}}\\\\\bold {v = 14.5{18 }}\\\\\bold {v = 0.805 m/s}$  

 

c )  Amplitude is the height of a wave which 9.5 m here.

To know more about amplitude,

https://brainly.com/question/17003906