Doppler Effect Calculator

Doppler Effect is evaluated from Source Frequency, Speed of Sound and Source Velocity. The calculation reports Observed Frequency, Frequency Shift and Observed Wavelength.

Results

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About the Doppler Effect Calculator

Doppler Effect is treated here as a quantitative relation between Source Frequency, Speed of Sound, Source Velocity and Observer Velocity and Observed Frequency, Frequency Shift, Observed Wavelength and Pitch Change.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
f_obs = f₀ x (v + v_o) / (v + v_s)
v_s: positive = source moving away, negative = approaching
v_o: positive = observer moving toward source, negative = moving away
For source approaching (v_s = -v_s_speed): denominator decreases → f_obs > f₀
For source receding (v_s = +v_s_speed): denominator increases → f_obs < f₀

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

f_obs = f₀ x (v + v_o) / (v + v_s)
v_s: positive = source moving away, negative = approaching
v_o: positive = observer moving toward source, negative = moving away
For source approaching (v_s = -v_s_speed): denominator decreases → f_obs > f₀
For source receding (v_s = +v_s_speed): denominator increases → f_obs < f₀

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Ambulance Siren Passing — Approach vs. Recede

Inputs

f_source: 700 v_sound: 343 v_source: -30 v_observer: 0
Observed Frequency: 767.09 Hz. Frequency Shift: 67.09 Hz. Observed Wavelength: 0.44714 m. Pitch Change: 9.58%

With Source Frequency = 700, Speed of Sound = 343, Source Velocity = -30 and Observer Velocity = 0 as the stated inputs, the result is Observed Frequency = 767.09 Hz, Frequency Shift = 67.09 Hz and Observed Wavelength = 0.44714 m. Each value corresponds to the declared output fields.

Example 2: Police Radar Speed Calculation

Inputs

f_source: 24125000000 v_sound: 299792458 v_source: -29.06 v_observer: 0
Observed Frequency: 24,125,002,338.53 Hz. Frequency Shift: 2,338.53 Hz. Observed Wavelength: 0.01243 m. Pitch Change: 0%

With Source Frequency = 24,125,000,000, Speed of Sound = 299,792,458, Source Velocity = -29.06 and Observer Velocity = 0 as the stated inputs, the result is Observed Frequency = 24,125,002,338.53 Hz, Frequency Shift = 2,338.53 Hz and Observed Wavelength = 0.01243 m. Each value corresponds to the declared output fields.

Example 3: Train Whistle at Grade Crossing

Inputs

f_source: 392 v_sound: 343 v_source: -22.35 v_observer: 0
Observed Frequency: 419.32 Hz. Frequency Shift: 27.32 Hz. Observed Wavelength: 0.81798 m. Pitch Change: 6.97%

With Source Frequency = 392, Speed of Sound = 343, Source Velocity = -22.35 and Observer Velocity = 0 as the stated inputs, the result is Observed Frequency = 419.32 Hz, Frequency Shift = 27.32 Hz and Observed Wavelength = 0.81798 m. Each value corresponds to the declared output fields.

Example 4: Moving Observer — Highway Chase

Inputs

f_source: 1000 v_sound: 343 v_source: 0 v_observer: 13.41
Observed Frequency: 1,039.1 Hz. Frequency Shift: 39.1 Hz. Observed Wavelength: 0.33009 m. Pitch Change: 3.91%

With Source Frequency = 1,000, Speed of Sound = 343, Source Velocity = 0 and Observer Velocity = 13.41 as the stated inputs, the result is Observed Frequency = 1,039.1 Hz, Frequency Shift = 39.1 Hz and Observed Wavelength = 0.33009 m. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate frequency shift heard as a train passes
  • Understand how police radar guns measure speed
  • Find the observed pitch of an ambulance siren approaching