> ## Documentation Index
> Fetch the complete documentation index at: https://otzr-mintlify-3a69404b.mintlify.site/llms.txt
> Use this file to discover all available pages before exploring further.

# Waves and Sound

> How energy travels across a room without anything really moving.

## The big idea (and it's weirder than it sounds)

Hold one end of a rope. Flick your wrist. A wave runs down the rope to the other end.

Here's the strange part: **no piece of the rope traveled from your hand to the other end.** Each tiny piece just went up and down a little. But the *pattern* moved.

That's what a wave is:

> **A wave is a pattern of energy moving through stuff — without the stuff itself going along for the ride.**

Water waves do the same thing. A duck floating on the ocean bobs up and down. The wave passes under it; the duck doesn't surf to shore.

## The vocabulary you actually need

<CardGroup cols={2}>
  <Card title="Wavelength (λ)" icon="ruler-horizontal">
    The distance from one peak to the next. Measured in meters.
  </Card>

  <Card title="Frequency (f)" icon="repeat">
    How many peaks pass a point each second. Measured in **hertz (Hz)** — one Hz = one wave per second.
  </Card>

  <Card title="Amplitude" icon="arrows-up-down">
    How tall the wave is. For sound, this is loudness. For light, this is brightness.
  </Card>

  <Card title="Speed (v)" icon="gauge-high">
    How fast the wave's pattern moves through the medium.
  </Card>
</CardGroup>

These tie together in one little equation that does a lot of work:

$v = f \cdot \lambda$

**Speed = frequency × wavelength.** If the speed is fixed (it usually is, for a given medium), then high frequency → short wavelength, and low frequency → long wavelength. Always a trade.

## Two flavors of waves

<AccordionGroup>
  <Accordion title="Transverse waves — wiggle sideways" icon="arrows-up-down">
    The stuff moves *across* the direction the wave is going. Like the rope: the wave goes forward, but each bit of rope moves up and down.

    Examples: water waves, light, waves on a string.
  </Accordion>

  <Accordion title="Longitudinal waves — squish and stretch" icon="arrows-left-right">
    The stuff moves *along* the same direction the wave is going. Imagine a slinky you push and pull at one end — compressions race down the spring.

    Examples: **sound**, seismic P-waves.
  </Accordion>
</AccordionGroup>

## Sound is just squished air

When you speak, your vocal cords vibrate. They push air molecules forward, which bump into the next ones, which bump into the next ones... A traveling pattern of "squished" and "stretched" air moves outward. When it reaches someone's ear, their eardrum gets pushed and pulled by those same compressions, and their brain interprets it as sound.

**Sound is a longitudinal wave in air** (or water, or steel, or anything with atoms).

### Why sound doesn't travel in space

No atoms = nothing to squish = no sound. In space, no one can hear you scream — because there's literally nothing between your mouth and another person's ear to carry the wave. Movies that make spaceships go *boom* are lying. Forgivably, but lying.

### Speed of sound, in different stuff

| Medium     | Speed of sound |
| ---------- | -------------- |
| Air (20°C) | 343 m/s        |
| Water      | ≈ 1,500 m/s    |
| Steel      | ≈ 5,000 m/s    |

Sound moves faster through tightly packed stuff because the atoms can hand off the vibration faster. Sound through air is slow enough that you see lightning before you hear the thunder — light travels almost instantly, sound takes about 3 seconds per kilometer.

## Pitch and loudness, in physics terms

* **Pitch** = frequency. High note = many vibrations per second. Low note = few. A human can hear roughly 20 Hz to 20,000 Hz.
* **Loudness** = amplitude. Big compressions = loud. Small compressions = quiet. Measured in **decibels (dB)**, which is a logarithmic scale (every 10 dB up is roughly 10× the intensity).

A whisper: ≈30 dB. Conversation: ≈60 dB. Concert: ≈110 dB. Jet engine: ≈140 dB. The decibel scale grows fast, which is why hearing damage sneaks up on people.

## The Doppler effect: why ambulances change pitch

You've heard it: an ambulance siren sounds high as it comes toward you, then drops in pitch as it passes.

Why? The siren makes a constant pitch. But as the ambulance moves *toward* you, each new sound wave is emitted from slightly closer than the last. The waves bunch up. Shorter wavelength = higher frequency = higher pitch.

As it moves *away*, the opposite happens: waves spread out, lower pitch.

This isn't a sound trick — it's true for *any* wave from a moving source. Astronomers use the Doppler effect on light from galaxies to figure out that the universe is expanding. Same idea as the ambulance, just with light instead of sound.

## Reflection, refraction, diffraction — quick tour

<Steps>
  <Step title="Reflection">
    Wave bounces off a surface. Echoes are sound waves reflecting off walls. Mirrors are light waves reflecting off silvered glass.
  </Step>

  <Step title="Refraction">
    Wave bends as it enters a different medium (because it changes speed). This is why a straw in a glass of water looks bent. Lenses bend light using refraction.
  </Step>

  <Step title="Diffraction">
    Wave spreads around obstacles or through openings. You can hear someone around a corner even if you can't see them — sound diffracts around corners more than light does (because sound has a longer wavelength).
  </Step>
</Steps>

## A useful mental model

Think of waves as a way to **move energy without moving stuff.** That's the trick the universe pulled. Sound carries the energy of your voice across a room. Light carries the energy of the Sun across the solar system. Radio carries energy and information to your phone.

No atom ever has to take the trip. The pattern does.

<Card title="Next: Electricity and Magnetism" icon="arrow-right" href="/physics/electricity-and-magnetism">
  The invisible force that runs your phone, your car, and your nervous system.
</Card>