Question

A pebble has an average diameter of 8 mm. Its \(\phi\)-value on the Udden-Wentworth scale is ___________ (answer in integer).

Hint:

Use \(\phi = -\log_2(d)\), with the diameter d in millimetres.

Answer 1

Correct Answer: -3

Step 1: Recall the phi scale formula.
The Udden-Wentworth scale describes grain size using the phi (\(\phi\)) value, defined as
\[ \phi = -\log_2(d) \]
where \(d\) is the grain diameter in millimetres. The minus sign means coarser grains get smaller, often negative, phi values, and finer grains get larger phi values.

Step 2: Put in the given diameter.
The pebble has a diameter of
\[ d = 8 \text{ mm} \]
so
\[ \phi = -\log_2(8) \]

Step 3: Simplify the logarithm.
Since \(8 = 2^3\),
\[ \log_2(8) = 3 \]
so
\[ \phi = -3 \]

Step 4: Final answer.
An 8 mm pebble has a phi value of \(-3\), which fits the pebble and gravel range on the Udden-Wentworth scale, where coarse fragments carry negative phi values.
\[ \boxed{\phi = -3} \]