5 A research student is using 3-D graph-plotting software to model a chain of volcanic islands in the Pacific Ocean. These islands appear above sea-level at regular intervals, (approximately) distributed along a straight line. Each island takes the form of a single peak; also, along the line of islands, the heights of these peaks decrease in size in an (approximately) regular fashion (see Fig. 1.1).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{06496165-0b83-4050-ae26-fa5a0614bd46-3_476_812_495_246}
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\caption{Fig. 1.1}
\end{figure}
The student's model uses the surface with equation \(\mathrm { z } = \sin \mathrm { x } + \sin \mathrm { y }\), a part of which is shown in Fig. 1.2 below. The surface of the sea is taken to be the plane \(z = 0\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{06496165-0b83-4050-ae26-fa5a0614bd46-3_789_951_1270_242}
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\caption{Fig. 1.2}
\end{figure}
- - Describe two problems with this model.
- Suggest revisions to this model so that each of these problems is addressed.
- Still using their original model, the student examines the contour \(z = 2\) for their surface only to find that the software shows what appears to be an empty graph.
Explain what has happened.