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Morse Code

Reference data and engineering information about morse code for mathematics applications.

morsecode

Overview

Engineering reference data for Morse Code in mathematics.

Key Formulas

Quadratic Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Roots of ax² + bx + c = 0.

Pythagorean Theorem

c2=a2+b2c^2 = a^2 + b^2

Right triangle relationship.

Circle Area

A=πr2A = \pi r^2

Area of a circle.

Logarithm

log⁡b(x)=ln⁡(x)ln⁡(b)\log_b(x) = \frac{\ln(x)}{\ln(b)}

Change of base formula.

Variables

Symbol Description Unit
π\pi Pi 3.14159...
ee Euler's number 2.71828...

Morse Code Character Reference

Morse Code Timing Formulas

The fundamental unit of time in Morse code is the dot duration (tdott_{dot}). All other timings are derived from it.

Core Timing Relationships

  1. Dash Duration: A dash is three times the length of a dot. tdash=3⋅tdott_{dash} = 3 \cdot t_{dot}

  2. Intra-character Spacing (between dots and dashes within a letter): The gap between elements within a single character is equal to one dot duration. telement−gap=tdott_{element-gap} = t_{dot}

  3. Inter-character Spacing (between letters): The gap between characters is equal to three dot durations. tchar−gap=3⋅tdott_{char-gap} = 3 \cdot t_{dot}

  4. Word Spacing: The gap between words is equal to seven dot durations. tword−gap=7⋅tdott_{word-gap} = 7 \cdot t_{dot}

Words Per Minute (WPM) Calculation

The standard word used for speed calculation is "PARIS", which has 50 dot units. The transmission speed in words per minute (SS) can be calculated from the dot duration in seconds:

S=1.2tdotS = \frac{1.2}{t_{dot}}

Conversely, you can find the required dot duration for a target speed:

tdot=1.2St_{dot} = \frac{1.2}{S}

Definitions

  • Dot (dit): The basic short signal unit in Morse code.
  • Dash (dah): A signal unit equal in length to three dots.
  • Element: A single dot or dash.
  • Character: A sequence of dots and dashes representing a letter, number, or punctuation mark (e.g., ...- is the character 'V').
  • Intra-character gap: The silent period between elements within a character, equal to one dot duration.
  • Inter-character gap: The silent period between characters within a word, equal to three dot durations.
  • Word gap: The silent period between words, equal to seven dot durations.

References