Phase-Shift Fraction Three-Row Scan - Waves, Oscillations, and Resonance Step by Step

Three phase rows divide path shift by wavelength so metre shifts become cycle fractions.

waves Against an 8 m wavelength, shifts 0 m, 2 m, and 4 m give cycle shifts 0, 1/4, and 1/2.

Example

Dividing path shift by wavelength turns metres into the cycle fraction that controls alignment. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Phase shift is path shift divided by wavelength

Two equal waves can be compared by how much one is shifted along the path. Divide that shift by wavelength to read the cycle fraction.

\text{cycle shift}=\Delta x/\lambda

No shift keeps crests aligned

A zero metre shift gives zero cycle shift, so matching crests stay matched.

\text{cycle shift}=\frac{\Delta x}{\lambda}=\frac{0\ \text{m}}{8\ \text{m}}=0

Quarter-cycle shift offsets the crests

A two metre shift against an eight metre wavelength is one quarter cycle.

\text{cycle shift}=\frac{\Delta x}{\lambda}=\frac{2\ \text{m}}{8\ \text{m}}=\tfrac{1}{4}

Half-cycle shift lines crest with trough

A four metre shift against the same wavelength is one half cycle, the cancellation alignment for equal waves.

\text{cycle shift}=\frac{\Delta x}{\lambda}=\frac{4\ \text{m}}{8\ \text{m}}=\tfrac{1}{2}

The same wavelength converts metres into cycle fraction

The wavelength column stays fixed. The shift column changes, and the cycle fraction follows exactly.

\begin{array}{c|c|c}\Delta x & \lambda & \Delta x/\lambda \\ \hline 0\ \text{m} & 8\ \text{m} & 0 \\ 2\ \text{m} & 8\ \text{m} & \tfrac{1}{4} \\ 4\ \text{m} & 8\ \text{m} & \tfrac{1}{2}\end{array}