Chapter 6.4, Problem 49E

To determine

To find: The type of transformation represented by $S$ and slope of a beach.

Answer to Problem 49E

The graph of $S$ is vertical translation $0.159$ units up and vertical stretch by a factor of $0.118$ of the graph of $f\left(d\right)$ .

Explanation of Solution

Given information: $S=0.159+0.118\log d$

  $\begin{array}{cc}Sandparticle& Diameter\left(mm\right),d\\ finesand& 0.125\\ mediumsand& 0.25\\ coarsesand& 0.5\\ verycoarsesand& 1\end{array}$

Calculation:

For fine sand,

  $\begin{array}{l}S=0.159+0.118\log 0.125\\ S\simeq 0.05\end{array}$

For medium sand,

  $\begin{array}{l}S=0.159+0.118\log 0.25\\ S\simeq 0.088\end{array}$

For coarse sand,

  $\begin{array}{l}S=0.159+0.118\log 0.5\\ S\simeq 0.123\end{array}$

For very coarse sand,

  $\begin{array}{l}S=0.159+0.118\log 0.1\\ S\simeq 0.159\end{array}$