The first proper test of the Doppler effect used a locomotive, a carriage full of horn players and a line of musicians standing beside the track between Utrecht and Maarssen. The first attempt was washed out by hail and snow, which made the horns impossible to play. When the experiment was run again in June, the listeners by the rails heard the approaching note half a tone high and the receding note half a tone low.
Half a tone is a number you can run backward. Put 440 Hz in, ask for the speed that turns it into a note half a step higher, and at 68 °F the answer is 21.86 mph. Nobody wrote down the air temperature that June day, so treat that as an estimate rather than a record. It is still a strikingly ordinary speed for an experiment that settled a scientific argument.
That is the thread of this piece. The physics that decided a railway experiment is the same physics that runs through an ordinary Saturday, so here is one, followed by the clock, from a cable in the morning to a star line at night.
7:10 a.m. The charger circuit
The day starts in the garage. A 40 A EV charger has to go on the far wall, and the panel is 120 ft away along the route the cable will actually take. The question sounds like a lookup. It is not.
Look up 40 A in an ampacity table and 8 AWG copper comes back, rated exactly 40 A. Run it through the voltage drop calculator and the same wire loses 7.47 V over the run, a drop of 3.11%. Over the 3% that is the usual target for a branch circuit. One size up, 6 AWG, drops 4.71 V, or 1.96%, and leaves 235.29 V at the charger.
There is a second check hiding in the charger. It runs for hours, so the circuit is sized at 125% of its current, which means 50 A. Put 50 A in and the answer is still 6 AWG: the drop rises to 2.46% and the usable ampacity of 55 A covers it. Both rules land on the same wire, which is the comfortable outcome.
Would aluminum do? It would, one size bigger: 4 AWG aluminum drops 2.03% on the same run. Lighter, cheaper, and fine as long as the terminals are rated for it.
Most runs are not exactly 120 ft, and the ready-made pages cover the common ones at 240 V: 30 A, 40 A, 50 A and 60 A at 100 ft; 30 A, 50 A and 60 A at 150 ft; 30 A and 50 A at 200 ft.
9:30 a.m. The shed, and a spool of 12 AWG
Next job: power to the garden shed, 100 ft from the house, on an ordinary 20 A, 120 V circuit. There is a spool of 12 AWG in the garage. It is rated for 20 A. Surely that settles it?
No. Over 100 ft at 20 A, 12 AWG drops 7.92 V, which is 6.60%, and the saw at the end of it sees 112.08 V. The wire also turns 158 W into heat along the way. The calculator's answer is 8 AWG: 3.11 V, 2.59%, 116.89 V at the outlet.
Ampacity says whether a wire will overheat. Voltage drop says whether the thing at the end will work properly. At 100 ft they give different answers, and the stricter one wins.
Move the shed to the back of the lot, 200 ft out, and it takes 4 AWG to hold the drop at 2.05%. Twice the distance cost two steps on the standard list, from 8 to 6 to 4. The 120 V pages for this kind of run: 15 A and 20 A at 100 ft, 20 A at 150 ft and 20 A at 200 ft.
12:15 p.m. A siren on the main road
An ambulance goes by on the main road at about 60 mph. Its siren sits around 700 Hz. What you hear is something else.
Coming toward you the pitch is 759.3 Hz, 8.48% higher than the siren itself. The moment it passes, the pitch drops to 649.3 Hz. That fall is 2.71 semitones, a little more than a whole tone on a piano, and it is the reason a passing siren sounds like it is sliding downhill.
The Doppler effect calculator asks for the air temperature because sound travels faster in warm air, 767.7 mph at 68 °F. The same siren at 7 a.m., at 41 °F, would have swung from 761.1 Hz to 648 Hz, a drop of 2.78 semitones. In the heat of the afternoon, at 86 °F, it would be 2.67. Small differences. Real ones.
Speed matters far more than temperature. At 30 mph the same siren drops only 1.35 semitones, about half as much. At the 21.86 mph worked out earlier the drop comes to 0.99 semitones, which is what the listeners by the Dutch railway described: half a tone up, half a tone down.
3:40 p.m. The radar gun at the edge of town
A radar gun sits by the road into town. It sends out a microwave beam, catches the reflection from each car and measures one thing: how much the frequency moved.
On a Ka-band gun at 34.7 GHz, a car closing at 65 mph comes back 6.727 kHz higher. Every mph is worth 103.49 Hz, so a car at 55 mph shows 5.692 kHz instead. The shift is doubled compared with a siren-style formula, because the car receives the beam at a shifted frequency and then sends that shifted signal back.
Run it backward, the way the gun does, and 6,727 Hz becomes exactly 65 mph. Aim the gun 10 degrees off the line of travel and it reads about 1.5% low. It never reads high for that reason, only low.
6:20 p.m. The heavy bag
Evening, and a boxing gym. How hard does a 20 mph punch land?
The punch force calculator needs three things: the speed of the fist, the mass that moves with it, and how long it stays in contact. With the typical effective mass of 2.9 kg and a contact of 12 ms, a 20 mph punch peaks at 3,394 N, or 763 lbf. That is 99% of the 3,427 N average measured for Olympic boxers throwing straight punches at an instrumented dummy head.
A heavy bag is softer than a dummy head, so the contact lasts longer. Stretch it to 20 ms and the same punch peaks at 2,036 N. Momentum is unchanged at 25.9 N·s; only the time it is spread over has changed. That is what padding is for.
Mass is the other lever, and people underrate it. The same 20 mph fist with only the arm behind it, 0.81 kg, lands at 948 N. With the body turned into it, 4.97 kg, the estimate climbs to 5,817 N. Throwing faster helps too: 25 mph with the typical mass gives 4,243 N.
10:05 p.m. A line in the spectrum
Last one. A backyard spectroscope on a telescope shows the red hydrogen line, which sits at 656.28 nm when nothing is moving. In the light from a fast-moving galaxy it shows up at 658.47 nm instead.
Same effect as the siren at noon, stretched to the speed of light: the source is moving away at 998.7 km/s. For objects that far away most of the redshift comes from the expansion of space rather than motion through it, so the number is a Doppler reading and nothing more. It is the same equation the horn players tested on a train, now applied to light from another galaxy.
The whole day in one table
Six moments, six questions, and what went into each answer.
| Time | The question | What went in | Answer |
|---|---|---|---|
| 7:10 a.m. | Which wire feeds the charger? | 40 A, 240 V, 120 ft, copper, 3% | 6 AWG, 1.96% drop |
| 9:30 a.m. | Is 12 AWG enough for the shed? | 20 A, 120 V, 100 ft, copper | No: 6.60%, needs 8 AWG |
| 12:15 p.m. | What does the siren do as it passes? | 700 Hz, 60 mph, 68 °F | 759.3 Hz down to 649.3 Hz |
| 3:40 p.m. | What did the radar gun actually measure? | Ka band 34.7 GHz, 65 mph | +6.727 kHz |
| 6:20 p.m. | How hard is a 20 mph punch? | 2.9 kg, 20 mph, 12 ms | 3,394 N peak |
| 10:05 p.m. | How fast is that star line moving? | 656.28 nm seen at 658.47 nm | 998.7 km/s away |
The same Saturday, done differently
Change one decision at each hour and the numbers move, some a lot and some hardly at all.
| What changes | As the day went | The alternative | What it shows |
|---|---|---|---|
| Charger feeder in aluminum | 6 AWG copper, 1.96% | 4 AWG aluminum, 2.03% | One size up, a cheaper cable |
| Shed fed from 200 ft instead of 100 ft | 8 AWG, 2.59% | 4 AWG, 2.05% | Twice the distance, two sizes up |
| Siren heard at 7 a.m., 41 °F | Drop of 2.71 semitones | Drop of 2.78 semitones | Cold air, slightly larger swing |
| Traffic at 55 mph instead of 65 | +6.727 kHz | +5.692 kHz | 103.49 Hz less per mph |
| Punch into a softer bag, 20 ms | 3,394 N | 2,036 N | Same momentum, spread out longer |
| Arm-only punch, 0.81 kg | 3,394 N | 948 N | Mass matters as much as speed |
The pattern is worth noticing. Distance and mass change answers by whole steps: two wire sizes, a punch more than three times weaker. Temperature and small speed changes move them by a few percent. When a result surprises you, look first at the input that scales hardest.
Numbers worth keeping
| Quantity | Value |
|---|---|
| Longest 120 V run at 3%, 15 A, 12 AWG copper | 60 ft |
| Same, 10 AWG / 8 AWG / 6 AWG | 96 ft / 154 ft / 244 ft |
| Radar shift per mph, X / K / Ka band | 31.39 / 72.02 / 103.49 Hz |
| Siren drop passing at 30 mph / 60 mph | 1.35 / 2.71 semitones |
| Olympic boxers, average straight punch | 3,427 N |
| Hydrogen-alpha at rest | 656.28 nm |
Tools discussed in this article
- Voltage drop calculator: the smallest copper or aluminum gauge that keeps the drop under your limit and still carries the current, with ready-made pages for 15 A, 20 A, 30 A, 40 A, 50 A and 60 A at 100 ft.
- Doppler effect calculator: the pitch you hear from a moving source, the shift a radar gun reads, and the redshift of a spectral line, or the speed behind any of them.
- Punch force calculator: peak and average force of a punch from hand speed, effective mass and contact time, set against measured Olympic punches.
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