Describe the electromagnetic spectrum as a family of transverse waves travelling at the speed of light in a vacuum, ordered by frequency and wavelength, and apply $c = f\lambda$ to electromagnetic waves.

What this topic is asking

This dot point places visible light within the wider electromagnetic spectrum. The Physical Setting/Physics course asks you to recognize that radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays are all the same kind of wave, transverse electromagnetic waves travelling at the speed of light in a vacuum, differing only in frequency and wavelength, and to apply the wave equation $c = f\lambda$ to them. The Regents tests the ordering of the spectrum and wave-equation calculations using $c$.

One family of waves

The key unifying idea is that radio waves and gamma rays are not different in nature, only in frequency. They are all electromagnetic waves, all transverse, all travelling at $c$ in a vacuum. This is why the same wave equation applies across the whole spectrum and why visible light is just the narrow band our eyes detect.

The order of the spectrum

Remembering this order is a standard Regents item. Radio waves have the lowest frequency and longest wavelength; gamma rays the highest frequency, shortest wavelength and most energy. The energy connection (higher frequency, more energetic) explains why ultraviolet, X-rays and gamma rays are more damaging to living tissue than radio waves or visible light, and it leads into the photon picture in the dual nature of light.

The wave equation for electromagnetic waves

For any electromagnetic wave in a vacuum, the wave speed is the speed of light, so the wave equation becomes

Because $c$ is fixed, frequency and wavelength are inversely related across the whole spectrum: a high-frequency gamma ray has a tiny wavelength, while a low-frequency radio wave has a long one. Given any one of frequency or wavelength, the other follows immediately from $c = f\lambda$. (In a medium other than a vacuum, electromagnetic waves slow to $v = c/n$, the basis of refraction.)

Reference Tables note

The Reference Tables list the speed of light $c = 3.00 \times 10^8$ m/s as a constant and include an electromagnetic spectrum chart (showing the bands and their frequencies and wavelengths) and a visible-light wavelength chart (the wavelengths of the colors). The wave equation $v = f\lambda$ is printed in the Waves section and is applied with $v = c$ for electromagnetic waves. You recall the order of the spectrum and that all electromagnetic waves are transverse and travel at $c$ in a vacuum.

Try this

Q1. State the speed of all electromagnetic waves in a vacuum. [1 point]

• Cue. $3.00 \times 10^8$ m/s (the speed of light).

Q2. A microwave has a frequency of $3.0 \times 10^9$ Hz. Calculate its wavelength in a vacuum ($c = 3.00 \times 10^8$ m/s). [2 points]

• Cue. $\lambda = \dfrac{c}{f} = \dfrac{3.00 \times 10^8}{3.0 \times 10^9} = 0.10$ m.