Physical Science · Unit 6: Waves · Elise's Elected Education

Imagine you're standing at the edge of a quiet pond. You drop a stone in the middle. Plunk. What happens?

You see those circular ripples spreading outward from where the stone hit. They move away from the center, getting wider and wider. The water itself doesn't actually travel outward — if there were a leaf on the surface, it would just bob up and down, not get carried away. The ripple moves. The water stays put.

That's a wave. Energy moving through stuff, without the stuff itself moving very far.

Now zoom in on one ripple. The high parts are called crests (peaks). The low parts are troughs (valleys). The distance from one crest to the next crest is the wavelength — basically, how long one full wave is. And how many waves pass a point each second is the frequency.

Sound is also a wave. When you yell, you push air molecules outward in waves. They bump into the next molecules, which bump into the next, and so on, until the wave reaches someone's ear. The ear vibrates. The brain hears "hey." But the air molecules themselves never travel from your mouth to their ear — they just jiggled back and forth in place.

Light is a wave too. But light is special: it doesn't need anything to travel through. Sound needs air (or water, or something physical). Light can travel through pure vacuum, which is how sunlight reaches us through space. Light is an electromagnetic wave.

And here's where it gets wild: light is just one tiny slice of a giant family of electromagnetic waves. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays — they are ALL the same thing. Same kind of wave. Just different frequencies. Your wifi router is shooting radio waves at you right now. Your eyes can't see those, but they're identical in nature to the light you DO see. Your eyes only happen to be tuned to one narrow band — what we call "visible light."

That's the secret of this unit: everything that ever traveled to you as a signal — your favorite song, the heat from the sun, your phone notification, the colors you see, your dentist's X-ray — they're all just waves. Same family. Different costumes.

Here's what a wave looks like, with the parts labeled:

crest crest
/\ /\
/ \ / \
/ \ / \
------\------/----
\ /
\ /
\/
trough
|<-- wavelength -->|

crests = high points · troughs = low points · wavelength = distance between two crests

The two main numbers that describe every wave:

WAVELENGTH (λ) = length of one full wave (meters)
FREQUENCY (f) = waves per second (Hertz, Hz)
VELOCITY (v) = how fast wave moves (m/s)

λ is the Greek letter "lambda" — physicists love Greek letters

The relationship between them is one of the simplest equations in physics:

v = f × λ

velocity = frequency × wavelength

Sound waves vs. light waves — they look similar but behave very differently:

SOUND: needs a medium (air/water) · ~340 m/s in air · longer wavelengths

LIGHT: needs nothing · 300,000,000 m/s · much shorter wavelengths

light is roughly 1,000,000 times faster than sound

The full electromagnetic spectrum — same wave family, sorted by wavelength (longest → shortest):

Radiowifi, AM/FM, cell phones

Microwavemicrowave ovens, radar

Infraredheat, TV remotes, night vision

Visiblered → orange → yellow → green → blue → violet (the only ones our eyes see)

UVsunburn, blacklights

X-raymedical imaging

Gammaradioactive decay, cancer treatment

Same waves, different wavelengths. As wavelength goes down, frequency (and energy) goes UP. Radio waves are gentle. Gamma rays are violent. Visible light sits comfortably in the middle.

To calculate the speed of any wave, use this equation. Always the same recipe:

Step 1. Find the FREQUENCY (how many waves per second, in Hertz).

Step 2. Find the WAVELENGTH (length of one wave, in meters).

Step 3. Plug into the equation:

v = f × λ

velocity (m/s) = frequency (Hz) × wavelength (m)

Step 4. Multiply. Label the answer in meters per second.

Worked example. A sound wave has a frequency of 100 Hz and a wavelength of 3.4 meters. What's its velocity?

v = f × λ
v = 100 × 3.4
v = 340 m/s

that's roughly the speed of sound in air at room temperature

Step 5. Rearrange if you need a different value: f = v / λ (find frequency) or λ = v / f (find wavelength).

Bonus rule for EM waves. All electromagnetic waves (radio, light, X-rays, etc.) travel at the same speed in vacuum: c = 3 × 10⁸ m/s (300 million m/s). So for any EM wave: c = f × λ. If you know one, you can find the other.

Waves: How Sound, Light, and Signals Travel

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