Question

For a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin $\frac{2\pi t }{T}$ , where a is the amplitude and T is the period of the wave in seconds.

Write an equation for the given function given the amplitude, period, phase shift, and vertical shift.
amplitude: 4, period = $4^{\pi }$ phase shift = $-\frac{4}{3}\pi$ vertical shift = -2

Answer 1

Answer:

  y = 4sin((t+4π/3)/2) -2

Step-by-step explanation:

The generic form is ...

  y = A·sin(B(t -C)) +D

where ...

• A is the amplitude
• B is 2π/period
• C is the phase shift
• D is the vertical shift

You have ...

• A = 4
• period = 4π, so B = (2π)/(4π) = 1/2
• C = -4π/3
• D = -2

Putting these values into the above form gives ...

  y = 4sin((t+4π/3)/2) -2

A graph is shown in the attachment.

Answer 2

Following are calcultion of the wave equation:

Given:

$\bold{amplitude\ (a)=4}\\\\\bold{period\ (T)=4\pi }\\\\\bold{phase \ shift\ (C)= -\frac{4\pi}{ 3}}\\\\\bold{vertical\ shift\ b=-2}$

To find:

function=?

Solution:

$\bold{amplitude\ (a)=4}\\\\\bold{period\ (T)=4\pi }\\\\\bold{phase \ shift\ (C)= -\frac{4\pi}{ 3}}\\\\\bold{vertical\ shift\ b=-2}$

Using formula:

$\therefore\\\\\to \bold{y= 2\sin (\frac{2\pi}{T}t +c) +b}$

Where  

T=period

c=phase shift

b=vertical shift

Putting the value in the above given function:

$\bold{f(t)=4 \sin (\frac{2\pi}{4\pi}t-\frac{4\pi}{3})-2}$

      $\bold{=4\sin(\frac{t}{2}-\frac{4\pi}{3})-2}$

Learn more:

brainly.com/question/14305080