Describe the electromagnetic spectrum as a range of waves with different wavelengths, frequencies, and energies, order its regions, and explain how devices use waves to transmit information (MA STE Introductory Physics, Waves, HS-PS4-3, HS-PS4-5).

What this topic is asking

The Massachusetts Introductory Physics MCAS closes the Waves module with the electromagnetic spectrum and how technology uses waves. You must describe the spectrum as a range of waves with different wavelengths, frequencies, and energies, order its regions, note that all of them travel at the speed of light, and explain how devices use waves to transmit information (HS-PS4-3 and HS-PS4-5). The crosscutting ideas are patterns (the orderly spectrum) and structure and function (different waves suit different jobs).

What the spectrum is

The single most important fact the MCAS tests is that these are all the same phenomenon at different frequencies, and all travel at the speed of light, $c = 3.0 \times 10^8$ m/s, which is on the reference sheet. They are transverse waves and, unlike sound, need no medium, so they cross the vacuum of space. Visible light is just the narrow band our eyes detect; the rest of the spectrum is invisible but just as real.

The order of the regions

The pattern is the thing to learn:

• Radio and microwaves: long wavelength, low energy; used for broadcasting, Wi-Fi, radar, and cooking.
• Infrared: felt as heat; used in remote controls and thermal imaging.
• Visible light: the thin band from red to violet that the eye sees.
• Ultraviolet: higher energy, causes sunburn; used in sterilization.
• X-rays and gamma rays: very short wavelength, very high energy; used in medical imaging and cancer treatment, and dangerous in large doses.

Because the speed is fixed at $c$, the wave equation $c = f\lambda$ means the higher-frequency regions automatically have shorter wavelengths.

Using waves to transmit information

This is the HS-PS4-5 part of the standard, and it asks you to explain how real devices use waves:

• Radio and television broadcast information on radio waves; the receiver tunes to the right frequency and decodes the signal.
• Cell phones and Wi-Fi use microwaves to carry data wirelessly.
• Fiber optics send pulses of light through thin glass fibers, kept inside by reflection, to carry internet and phone data at high speed.
• Radar and ultrasound use reflected waves (radio and sound, respectively) to detect objects and form images.

The common thread is that the wave is the carrier, and information rides on it by changing some feature of the wave, then is recovered at the other end.

Worked example

Reference-sheet note

The reference sheet gives the wave equation $v = f\lambda$ and the constant speed of light $c = 3.0 \times 10^8$ m/s, which together let you find any EM wavelength from its frequency. What you recall is the order of the regions (radio to gamma rays), that shorter wavelength means higher frequency and energy, that all EM waves travel at $c$ and need no medium, and how devices encode information onto waves and decode it at the receiver.

Try this

Q1. List the electromagnetic spectrum from longest to shortest wavelength. [2]

• Cue. Radio, microwave, infrared, visible light, ultraviolet, X-rays, gamma rays.

Q2. A microwave has a frequency of $1.0 \times 10^{10}$ Hz. Using $c = 3.0 \times 10^8$ m/s, calculate its wavelength. [2]

• Cue. $\lambda = \dfrac{c}{f} = \dfrac{3.0 \times 10^8}{1.0 \times 10^{10}} = 3.0 \times 10^{-2}$ m (0.03 m).