Velocity, Frequency, and Wavelength

Source: Radiation, Light and Illumination - Location: Lecture I formula OCR needs verification View source record

Modern Form

$$S = f \lambda$$ $$f = \frac{S}{\lambda}$$ $$\lambda = \frac{S}{f}$$

Variables

• S: speed of propagation.
• f: frequency.
• lambda: wavelength.

Steinmetz Example

Using S = 3 x 10^10 cm/s, a 60-cycle alternating current gives:

$$\lambda = \frac{3 \times 10^{10}}{60} = 5 \times 10^8\ \text{cm}$$

That is about 5,000 km, or about 3,100 miles.

Physical Meaning

This relation is the bridge between ordinary power frequency, wireless waves, Hertzian waves, infrared, visible light, ultraviolet, and X-rays.

Why Steinmetz Starts Here

This equation lets Steinmetz make an unusually broad move in the opening lecture: he places slow electrical alternations, wireless waves, visible light, ultraviolet radiation, and X-rays onto one continuum. The quantities differ enormously in frequency and wavelength, but the same propagation relation ties them together.

That is why this simple relation is foundational for the archive. It connects the radiation book to electric waves, spectrum diagrams, transmission-line phenomena, and the later wave/surge material.

Unit Translation

Steinmetz’s first source uses centimeter-second language. A modern SI translation usually writes:

$$c = f\lambda$$

with:

• c in meters per second,
• f in hertz,
• \lambda in meters.

The historical relation is the same, but the numerical scale changes with units. Mature equation pages should show the original unit system before converting.

Worked Modern Example

For a 60 Hz alternating quantity using c = 3.0 x 10^8 m/s:

$$\lambda = \frac{3.0 \times 10^8}{60} = 5.0 \times 10^6\ \text{m}$$

That is 5,000 km, matching the historical scale when centimeters are converted to kilometers.

Conceptual Reading

The equation is simple, but the conceptual consequence is large: frequency is not just a circuit label and wavelength is not only an optics label. Together they let Steinmetz describe electrical waves and visible light as members of a wider radiation scale.

Research Routes

Read Lecture I sourceOpen the source text where the frequency-wavelength bridge begins.Open radiation visualsSee the spectrum guide, source visual map, figure candidates, and related formulas.Open Electric WavesTrace the concept side of this relation through the corpus.Open wave visualizerUse the interactive tool as a modern explanation aid.

Verification Needs

• Verify the exact symbol Steinmetz prints for velocity in Lecture I.
• Confirm the numerical wavelength example against the scan, including units and rounding.
• Link the equation to the original spectrum table and Fig. 14 crop after final page verification.