Keep source and observer velocities in the medium frame
Sound fronts move through a medium. In this model still air carries waves toward +x at 340 m/s, the source is left of the observer and the source frequency is 500 Hz. Positive source velocity moves toward the observer; positive observer velocity moves away along the same direction. Keeping these signs explicit is more reliable than choosing a formula sign from an unlabeled word such as approaching.
Learning outcome: Compare (vs,vo)=(20,0),(0,−20),(20,20) and (−20,0) m/s. Predict whether each shift is upward, absent or downward. Retain wavelength and front-crossing speed separately before forming the observed frequency.
Starting recap
Separate local oscillation from propagation, amplitude from its square, and a calibration fit from a fresh prediction. Use declared phase, medium frame and boundary conditions.
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Try
For vs=20 m/s and vo=0, wavelength is (340−20)/500=.64 m and observed frequency is 531.25 Hz. If instead the source is stationary and the observer moves at −20 m/s, frequency is 500(360/340)≈529.412 Hz despite the same 20 m/s closing speed.
Open the experimentPredict
Which pair gives no Doppler shift under the stated collinear still-air model?
Experiment
Compare (vs,vo)=(20,0),(0,−20),(20,20) and (−20,0) m/s. Predict whether each shift is upward, absent or downward. Retain wavelength and front-crossing speed separately before forming the observed frequency.
Keep both velocities in the medium frame
Worked teaching model · synthetic values · Source is left of observer; waves travel +x through still uniform air at 340 m/s. Source emits 500 Hz in this classical medium model. Positive observer velocity moves away along propagation. Snapshot before crossing; all speeds subsonic. Not a light or relativistic Doppler law.
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Received frequency versus observer medium-frame velocity
Unlike graph quantities rescale independently; read units and values, not screen angles. 1: fixed source velocity (solid). Joined curves show the supplied model, not additional observations.
Equivalent numerical coordinates for Received frequency versus observer medium-frame velocity
fixed source velocity
| observer velocity +x (m/s) | received frequency (Hz) |
|---|---|
| -40 | 593.75 |
| -39 | 592.188 |
| -38 | 590.625 |
| -37 | 589.063 |
| -36 | 587.5 |
| -35 | 585.938 |
| -34 | 584.375 |
| -33 | 582.813 |
| -32 | 581.25 |
| -31 | 579.688 |
| -30 | 578.125 |
| -29 | 576.563 |
| -28 | 575 |
| -27 | 573.438 |
| -26 | 571.875 |
| -25 | 570.313 |
| -24 | 568.75 |
| -23 | 567.188 |
| -22 | 565.625 |
| -21 | 564.063 |
| -20 | 562.5 |
| -19 | 560.938 |
| -18 | 559.375 |
| -17 | 557.813 |
| -16 | 556.25 |
| -15 | 554.688 |
| -14 | 553.125 |
| -13 | 551.563 |
| -12 | 550 |
| -11 | 548.438 |
| -10 | 546.875 |
| -9 | 545.313 |
| -8 | 543.75 |
| -7 | 542.188 |
| -6 | 540.625 |
| -5 | 539.063 |
| -4 | 537.5 |
| -3 | 535.938 |
| -2 | 534.375 |
| -1 | 532.813 |
| 0 | 531.25 |
| 1 | 529.688 |
| 2 | 528.125 |
| 3 | 526.563 |
| 4 | 525 |
| 5 | 523.438 |
| 6 | 521.875 |
| 7 | 520.313 |
| 8 | 518.75 |
| 9 | 517.188 |
| 10 | 515.625 |
| 11 | 514.063 |
| 12 | 512.5 |
| 13 | 510.938 |
| 14 | 509.375 |
| 15 | 507.813 |
| 16 | 506.25 |
| 17 | 504.688 |
| 18 | 503.125 |
| 19 | 501.563 |
| 20 | 500 |
| 21 | 498.438 |
| 22 | 496.875 |
| 23 | 495.313 |
| 24 | 493.75 |
| 25 | 492.188 |
| 26 | 490.625 |
| 27 | 489.063 |
| 28 | 487.5 |
| 29 | 485.938 |
| 30 | 484.375 |
| 31 | 482.813 |
| 32 | 481.25 |
| 33 | 479.688 |
| 34 | 478.125 |
| 35 | 476.563 |
| 36 | 475 |
| 37 | 473.438 |
| 38 | 471.875 |
| 39 | 470.313 |
| 40 | 468.75 |
At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.
| Quantity | Value | Unit |
|---|---|---|
| Ahead-of-source wavelength | 0.64 | m |
| Received frequency | 531.25 | Hz |
| Observed-minus-source frequency | 31.25 | Hz |
| Wave speed relative to observer | 340 | m/s |
| Source-observer relative velocity | 20 | m/s |
Source motion changes the wavelength; observer motion changes the rate of crossing those fronts.
Successive fronts are emitted one source period apart while the source advances vs/fs, so lambda=(c−vs)/fs ahead of it. The observer crosses fronts at relative speed c−vo, giving fobs=fs(c−vo)/(c−vs). Equal source and observer velocities cancel the shift in this collinear arrangement. Equal relative velocities alone do not generally give equal shifts when their separate medium-frame velocities differ. A moving medium requires transforming both velocities consistently; this formula is not the relativistic light result.
Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.
Source motion changes the wavelength; observer motion changes the rate of crossing those fronts.
Successive fronts are emitted one source period apart while the source advances vs/fs, so lambda=(c−vs)/fs ahead of it. The observer crosses fronts at relative speed c−vo, giving fobs=fs(c−vo)/(c−vs). Equal source and observer velocities cancel the shift in this collinear arrangement. Equal relative velocities alone do not generally give equal shifts when their separate medium-frame velocities differ. A moving medium requires transforming both velocities consistently; this formula is not the relativistic light result.
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