Explain wave behaviors, relate speed, frequency and wavelength, compare mechanical and electromagnetic waves, order the electromagnetic spectrum, and describe the Doppler shift

Learning goal: Describe reflection, refraction, absorption, diffraction and superposition conceptually and give examples for sound and for radiant energy; relate the speed, frequency and wavelength of a wave from investigation data; compare mechanical waves, which need a medium, with electromagnetic waves, which do not; place the bands of the electromagnetic spectrum in order of energy, frequency and wavelength; explain what opaque, transparent, rough and smooth materials do to radiant energy; and describe the Doppler shift for sound and its role in the redshift of distant galaxies.

What a wave is and how it is measured. A wave carries energy from one place to another without carrying matter along with it. Middle school described waves by speed, wavelength, frequency and amplitude, and applied the ideas to seismic waves in different materials. Wavelength (λ) is the distance from one crest to the next, in meters; frequency (f) is the number of complete waves passing a point each second, in hertz (Hz); amplitude is the maximum displacement from rest, which is related to the energy carried; and speed (v) is how fast a crest travels through the medium. For any wave, speed equals frequency times wavelength, v = f λ, because f crests each of length λ pass a point every second. The speed of a wave is set by the medium it travels through, not by the source. That single fact decides what happens when frequency changes: in a given medium, raising the frequency shortens the wavelength, and the speed stays the same. A long spring stretched on the floor shows it. Shaking one end at 2.0 Hz gives waves 1.5 m apart, so v = 2.0 × 1.5 = 3.0 m/s. Shaking at 3.0 Hz on the same spring at the same tension gives waves 1.0 m apart, and v = 3.0 × 1.0 = 3.0 m/s again: the speed did not change, the wavelength did. For a spring, a string or sound in air, only changing the medium, such as stretching the spring tighter, changes the speed (in some media, such as deep water, waves of different frequency do travel at different speeds).

Mechanical and electromagnetic waves. A mechanical wave needs a medium, a material whose particles pass the disturbance along: sound in air, water, steel or rock, waves on a spring or a rope, seismic waves in Earth. No medium, no wave, which is why sound cannot cross a vacuum. Radiant energy travels as electromagnetic waves, which need no medium; light from the sun crosses empty space. Sources of light energy such as the sun or a bulb radiate continuously in all directions. All electromagnetic waves travel at the same speed in a vacuum, the speed of light, and slow slightly in materials such as glass or water. Sound in air at room temperature travels at roughly 340 m/s, almost a million times slower, which is why lightning is seen before thunder is heard.

Five behaviors. When a wave meets a new material, several things can happen, and they are described here in words, not equations. Reflection: the wave bounces off a barrier. Sound reflects as an echo; light reflects from a mirror. For a smooth, shiny surface the reflected light stays organized and forms a clear image; for a rough surface it scatters in all directions, a diffuse reflection, which is why you can see a page from any angle but cannot see your face in it. Refraction: the wave's speed changes as it passes from one medium into another, and when it meets the boundary at a slant its direction changes too (a wave arriving head-on changes speed but carries straight on), which is why a straw in water looks bent and why sound bends over a lake on a cool evening. Absorption: the material takes in the wave's energy and transforms it to another form, usually thermal energy; a black car roof in sunlight absorbs radiant energy and warms. Diffraction: the wave spreads out around a small obstacle or through a narrow opening, which is why you hear a conversation through a doorway before you can see the speakers. Superposition: when two waves traveling through the same medium meet, they pass through each other and continue unchanged; while they overlap, their displacements add, giving constructive interference (crest on crest, a bigger crest) or destructive interference (crest on trough, canceling). Two speakers playing the same note produce spots in a room where the sound is louder and spots where it is quieter for this reason. Sound shows all five behaviors; so does radiant energy.

Opaque, transparent, rough, smooth. For an opaque object such as paper, a chair or an apple, little if any radiant energy is transmitted through it; the energy is absorbed, warming the object, or reflected, and the mix of colors reflected is the color we see. For a transparent material such as glass or clear water, most of the energy is transmitted through, with smaller amounts absorbed or reflected. Rough versus smooth decides whether reflection is diffuse or image-forming. A material can be different for different bands: ordinary glass transmits visible light but absorbs most of the ultraviolet that causes sunburn, which is why you rarely sunburn through a closed window, although longer-wavelength ultraviolet (UVA) still passes and can harm skin and eyes over time.

The electromagnetic spectrum. Radiant energy comes in a wide range of frequencies, wavelengths and energies arranged into the electromagnetic spectrum. In order from lowest energy to highest: radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Along that same order the frequency rises and the wavelength shortens, and within visible light the order runs red, orange, yellow, green, blue, violet from lower to higher energy. The relative positions are what matter here; the exact frequency or wavelength ranges of each band are not needed. Radiant energy arrives in tiny packets called photons, and higher-frequency radiation carries more energy per photon, which is why ultraviolet can damage skin cells while the radio waves around us every day pass through you without harming cells (very intense radio or microwave radiation, such as inside a microwave oven, can still heat tissue), and why X-rays can pass through soft tissue but are absorbed by bone to form an image. Total radiant energy depends on more than frequency: a bright red lamp can deliver more total energy than a dim blue one, because the amount of radiation matters as well as the type. Each band has everyday uses: radio and microwaves carry broadcasts and phone signals, infrared is felt as warmth from a heater and used in remote controls, visible light is what we see, ultraviolet is used to sterilize surfaces, X-rays image bones, and gamma rays are used in some cancer treatments. Sound waves are used in medicine as well: ultrasound images an unborn baby by reflecting high-frequency sound from tissue boundaries.

Doppler shift. When a wave source and an observer move relative to each other, the observed frequency changes. If the source moves, the waves it sends ahead are bunched and those behind are spread out, so the wavelength changes too; if only the observer moves, the wavelength in the medium is unchanged, but the observer meets crests more or less often. Either way the direction of the shift is the same: when source and observer approach each other the observed frequency is higher, and when they move apart it is lower. For a moving source this goes with a changed wavelength: the waves an approaching source sends toward the observer are bunched to a shorter wavelength, and those from a receding source are stretched to a longer one. This is the Doppler shift, and an ambulance siren shows it: the pitch is higher as it approaches and drops as it passes and moves away, even though the siren itself never changes. The source frequency is unchanged; only what the observer receives is shifted. The same effect applies to light. Light from distant galaxies is shifted toward the longer, redder wavelengths, the redshift, which is evidence that those galaxies are moving away from us and that the universe is expanding. Calculating the size of the shift is not part of this course; the direction and the reasoning are.

A technology to weigh up. The relationship between frequency and wavelength applies directly to cell phones, which send and receive radio and microwave signals: a higher-frequency signal has a shorter wavelength in air, which affects how far it travels and how well it passes around and through obstacles by diffraction and absorption. The technology has beneficial aspects, such as emergency calls from anywhere with signal, navigation and access to information, and harmful aspects, such as distraction while driving or crossing roads, which is well documented, and disrupted sleep from late-night use. The radio and microwave energy the phone emits sits at the low-energy end of the spectrum, far below ultraviolet, and is too low in energy per photon to break chemical bonds the way ultraviolet or X-rays can; questions about other long-term effects are studied by health agencies, and a careful claim states what the evidence does and does not show rather than asserting either safety or harm beyond it.

Investigation: speed, frequency and wavelength on a spring. Materials: a long coil spring (a toy slinky), a floor tape measure, a stopwatch, two students, masking tape. Steps: stretch the spring to a marked length of 4.0 m on a smooth floor and keep that length fixed for the whole trial; one student shakes an end side to side steadily while the other counts shakes for 10 s to get the frequency; take a photo or mark with tape the positions of two neighboring crests to measure the wavelength; repeat at a slower and a faster shaking rate at the same length; then repeat one frequency with the spring stretched to 5.0 m. Record: for each trial the length, the frequency, the wavelength and the product f × λ. A result that supports the claim: at a fixed length the product f × λ is about the same for every frequency, so raising the frequency shortens the wavelength and leaves the speed unchanged; changing the length (the medium's tension) changes the product. Safety: do not let go of a stretched spring, keep it low to the floor, and do not overstretch it. What the model cannot show: a hand-shaken spring gives only rough frequencies, the crests are hard to freeze without a photo, and the spring shows a transverse mechanical wave, so it cannot model how an electromagnetic wave travels without a medium or how light's color relates to wavelength; those ideas come from other evidence.

Worked example 1 — speed from frequency and wavelength. A student shakes a spring at 2.0 Hz and measures crests 1.5 m apart. v = f λ = 2.0 Hz × 1.5 m = 3.0 m/s. At 3.0 Hz on the same stretched spring the wavelength is measured as 1.0 m, and v = 3.0 × 1.0 = 3.0 m/s. The claim supported by these data: for a fixed medium the speed is constant, so a higher frequency means a shorter wavelength; the evidence is the equal products.

Worked example 2 — a sound wavelength. Sound travels at about 340 m/s in room-temperature air. A 500 Hz note has wavelength λ = v ÷ f = 340 ÷ 500 = 0.68 m. A 170 Hz note has λ = 340 ÷ 170 = 2.0 m. The lower note has the longer wavelength, and both travel at the same speed because they are in the same air. In warmer air, sound travels faster, so both wavelengths would be a little longer.

Worked example 3 — sort behaviors. An echo from a cliff: reflection of sound. Hearing music around a corner: diffraction. A pencil looking bent in a glass of water: refraction of light at the water surface. A dark shirt warming in the sun: absorption, radiant energy becoming thermal energy. Two overlapping ripples on a pond making a taller ripple where crests meet: superposition with constructive interference. Each is a wave behavior, and each happens for both sound and radiant energy; the pencil example is light, but sound refracts too when it passes between warm and cool air.

Worked example 4 — order the spectrum and reason about energy. Which carries more energy per photon, ultraviolet or microwaves? The order from lowest to highest energy is radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma, so ultraviolet is higher in energy and in frequency, and shorter in wavelength. That is why brief exposure to ultraviolet can sunburn skin while a microwave signal from a phone tower does not. It does not follow that any ultraviolet source delivers more total energy than any microwave source; total radiant energy also depends on how much radiation is emitted.

Worked example 5 — Doppler direction. A train sounds its horn at a steady frequency while passing a station at speed. A person on the platform hears a higher pitch as the train approaches, because the sound waves reaching the ear are bunched to a shorter wavelength and so arrive at a higher frequency; after the train passes, the waves are stretched, the wavelength is longer and the pitch is lower. The horn's own frequency never changed. Light from a galaxy moving away from us is shifted the same way toward longer wavelengths, the redshift.

Representation task: a comparison model and a spectrum strip. Draw a two-column model comparing mechanical and electromagnetic waves: what carries the wave (a medium; no medium needed), examples (sound, spring, seismic; radio, light, X-rays), speed (set by the medium; the same for all bands in a vacuum) and how each is detected. Below it, draw a strip of the electromagnetic spectrum with the seven bands in order from radio to gamma, arrows labeled "energy and frequency increase" and "wavelength increases" pointing opposite ways, and the colors of visible light in order inside the visible band.

Demonstration task: research and present one wave phenomenon. Choose one observable wave phenomenon (an echo, a straw that looks bent in water, sound heard around a corner, two speakers producing loud and quiet spots, a shiny versus a matte surface in a flashlight beam, or a siren's changing pitch), research how it arises, and design a two-minute demonstration to present to the class using safe classroom materials. The presentation must name the behavior (reflection, refraction, absorption, diffraction, superposition or Doppler shift), show it, and state one thing the demonstration cannot show.

Independent performance: investigate and argue from evidence. Carry out the spring investigation and write an argument. Success criteria: the data table has at least three frequencies at one fixed length with wavelength and the product f × λ for each; the claim states what happens to wavelength and to speed when frequency is increased, and the evidence cites the numbers; one trial at a different length is used to show what does change the speed; a paragraph applies the same relationship to a phone signal, explaining that a higher-frequency signal has a shorter wavelength in air and discussing one benefit and one concern about phone use, with the concern stated carefully in terms of what is and is not known to you; and a final paragraph names two things the spring model cannot show about electromagnetic waves.