Interference

Multiple waves can be in the same position at the same time. Unlike particles, waves pass through each other without interacting.

Ears are able to detect separate sound frequencies, even though they enter the ear in a superposition. This spectrogram lets you visualize the frequencies that make up various sounds.

The Wedge is a famous surf spot that has some dangerously fun waves because of interference from waves reflected off a jetty.

Part of what makes music sound good depends on the background of the listener. Not everyone likes the same music, but some parts of music are universal. Western classical music is organized around 12 notes called the chromatic scale. Each note represents a specific frequency. In superposition the frequencies of these notes can form ratios that fit together nicely.

Music theory explores how to craft groups and sequences of notes. It's interesting that you can evoke emotions by adjusting the ratio between note frequencies.

For example, the major scale is a collection of 7 notes that can sound bright and stable together partly because they have a simple ratio between frequencies. Minor chords are collections of notes that might feel sad or tense partly because of the complex ratio between frequencies.

Diffraction

Waves tend to spread out in every direction possible within their medium. Diffraction is when a wave spreads out after some of the wave hits a barrier. This explains how sound can be heard around a corner even when there is no direct path.

Diffraction can be explained by thinking of every point on a wavefront as the source of spherical waves. These spherical waves interfere with each other to produce different patterns.

You can see examples of diffraction in these 2-D ripple tank simulations:

Single Slit: Waves spread out in a circle as they pass through a gap.
Double Slit: Notice the pattern of constructive and destructive interference.
Half Plane: Waves curve around a wall.
Obstacle: Waves of the right wavelength can almost ignore a small barrier.

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The Doppler Effect

The Doppler effect is heard when a source of sound moves past an observer as a "vvvVVVRRROOOMMMmmm". The observed sound drops in frequency very quickly as the source zooms past.

A sonic boom occurs when the source of sound is moving at the speed of sound. Can you produce a sonic boom in the simulation above?

Resonance

Rigid solids oscillate. They move back and forth at a consistent rhythm. Springs, bridges, buildings, wine glasses, and musical instruments all oscillate. We also see oscillation in lasers, atoms, electric circuits, orbits, swing sets, and pendulums.

Systems that oscillate have a natural frequency for their vibrations determined by properties like density, length, and rigidity. This is the frequency they most easily oscillate at.

An applied force that matches the natural frequency produce unusually high amplitude oscillations. This applied force is said to be resonant with the natural frequency of the system. This means the force pushes left as the system moves left, and right as the system moves right. It doesn't fight the natural motion of the system.

Standing Waves

A standing wave is a wave that oscillates in time, but does not move through space. Standing waves occur in most musical instruments in the form of vibrating strings or columns of air. You can produce a standing wave if you shake a string at just the right frequency while someone else holds the other end still.

Standing waves occur when two waves moving in opposite directions interfere with each other. This often occurs with reflected waves in a cavity, like a pipe. You can see a standing wave clearly in a Rubens' Tube.

The trick to a standing wave is that they only work at specific wavelengths in a medium with a reflective boundary. At most wavelengths the reflected waves interfere with themselves destructively to produce a superposition of nearly zero. It's like adding hundreds of random numbers between -1 and 1. Most of the time all the numbers cancel out and produce a result close to zero.

But, when a wavelength fits evenly into a closed region the reflected waves align. The superposition of all the reflected waves then produces alternating constructive and destructive interference patterns, a standing wave. This is another example of resonance.

This simulation calculates 64 reflections in a bounded region. Red waves are moving left. Blue waves are moving right. The black wave is the superposition of the reflections.