Exploring JF and SEF Functions

In this analysis:

• JF (Jongkees' Formula): Represents Jongkees' Formula.
• SEF (Strong Ear Formula): Represents the Strong Ear Formula.
• f: The ratio of "weak ear" relative to "strong ear". It is a dimensionless parameter where \( 0\% \leq f \leq 100\% \).

Formulas

The functions are defined as:

\( \quad \quad \text{JF} = \frac{1 - f}{1 + f} \quad \quad \quad \text{SEF} = 1 - f \)

Expressed in terms of each other:

\( \quad \quad \text{SEF}(\text{JF}) = \frac{2 \times \text{JF}}{1 + \text{JF}} \quad \quad \quad \text{JF}(\text{SEF}) = \frac{\text{SEF}}{2 - \text{SEF}} \)

Differences:

\( \quad \quad \text{SEF} - \text{JF} = \frac{\text{JF}(1 - \text{JF})}{1 + \text{JF}} \quad\) as a function of \( \text{JF} \)

\( \quad \quad \text{SEF} - \text{JF} = \frac{\text{SEF}(1 - \text{SEF})}{2 - \text{SEF}} \quad \) as a function of \( \text{SEF} \)

Graphs of SEF(f) and JF(f)