MCPCalc

Doppler Effect Calculator

Compute classical observed frequency, wavelength shift, and an optional relativistic correction.

Scratchpad (not saved)

Hz
m/s
m/s
m/s

What This Calculator Does

This calculator compares the emitted and observed frequency of a moving source-observer pair using the classical wave Doppler formula, then optionally adds a relativistic line-of-sight estimate. Positive source and observer speeds are treated as motion toward each other.

It combines Source Frequency, Source Velocity Toward Observer, Observer Velocity Toward Source, Medium Speed to estimate Observed Frequency, Percent Shift, Observed Wavelength.

Formula & Method

Core equations: Classical Doppler shift is f′=fv+vov−vsf'=f\frac{v+v_o}{v-v_s}, wavelength is λ=vf\lambda=\frac{v}{f}, and the relativistic correction for line-of-sight motion is f′=f1+β1−βf'=f\sqrt{\frac{1+\beta}{1-\beta}} where β=uc\beta=\frac{u}{c}.

Notation used in the formulas: RR = Observed Frequency; x1x_{1} = Source Frequency; x2x_{2} = Source Velocity Toward Observer; x3x_{3} = Observer Velocity Toward Source; x4x_{4} = Medium Speed; x5x_{5} = Relativistic Correction.

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it for quick acoustics or wave-propagation estimates when a source and observer move through a medium, or when comparing the size of the classical and relativistic shifts.

Reference Book

University Physics with Modern Physics

Hugh D. Young and Roger A. Freedman · Pearson

A common undergraduate physics text covering mechanics, electricity, waves, energy, and introductory modern physics.

View Book

Inputs Used

  • Source Frequency: Used directly in the calculation.
  • Source Velocity Toward Observer: Used directly in the calculation.
  • Observer Velocity Toward Source: Used directly in the calculation.
  • Medium Speed: Used directly in the calculation.
  • Relativistic Correction: Used directly in the calculation.

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