Chapter 12.7, Problem 29PPS

a.

To determine

To find: Equation of given model.

Answer to Problem 29PPS

Equation of given situation is

  $h=\sin \pi t$

Explanation of Solution

Given information:

Frequency of Earthquake wave $=0.5$ hertz

Amplitude $=a=1$

We need to write equation using Sine model.

Given

  $a=1$

Frequency of earthquake wave $=0.5$ hertz

We know

Period $=\frac{1}{frequency}$

  $\Rightarrow$ Period $=\frac{1}{0.5}$

  $\Rightarrow$ Period $=2$

  $\begin{array}{l}\Rightarrow \frac{2\pi }{b}=2\\ \Rightarrow b=\frac{2\pi }{2}\\ \Rightarrow b=\pi \end{array}$

Given it is Sine function.

Therefore,

On substituting values

We get

  $\begin{array}{l}y=a\sin bx\\ \Rightarrow h=1\sin \pi t\\ \Rightarrow h=\sin \pi t\end{array}$

Therefore,

Equation of given situation is

  $h=\sin \pi t$

b.

To determine

To find: Graph of the function and then determine the height of the wave after $20.5$ second.

Answer to Problem 29PPS

Height of the wave after $20.5$ seconds is $1$ meter.

Explanation of Solution

Given information:

Frequency of Earthquake wave $=0.5$ hertz

Amplitude $=a=1$

We need to write equation using Sine model.

  $t=20.5$

Equation of given situation is

  $h=\sin \pi t$

On substituting $t=20.5$ seconds

We get

  $\begin{array}{l}h=\sin \pi t\\ \Rightarrow h=\sin 20.5\times \pi \\ \Rightarrow h=\sin 20.5\pi \\ \Rightarrow h=1\end{array}$

Therefore,

Height of the wave after $20.5$ seconds is $1$ meter.

Graph of the function is