Waves can pass through each other. When they do, their displacements add together at each point. This is called the principle of superposition. It is a property of waves but not of particles.

《 LOOKING BACK Sections 16.1, 16.2, 16.3, and 16.4 Properties of traveling waves

A standing wave is created when two waves travel in opposite directions between two boundaries.

• Standing waves have well-defined patterns called modes.

• Some points on the wave, called nodes, do not oscillate at all.

The notes played by musical instruments are standing waves.

• Guitars have string standing waves.

• Flutes have pressure standing waves.

Changing the length of a standing wave changes its frequency and the note played.

《 LOOKING BACK Section 16.5 Sound waves

When two sources emit waves with the same wavelength, the overlapped waves create an interference pattern.

• Constructive interference (red) occurs where waves add to produce a wave with a larger amplitude.

• Destructive interference (black) occurs where waves cancel.

The superposition of two waves with slightly different frequencies produces a loud-soft-loud-soft modulation of the intensity called beats. Beats have important applications in music, ultrasonics, and telecommunications.

Superposition and standing waves occur often in the world around us, especially when there are reflections. Musical instruments, microwave systems, and lasers all depend on standing waves. Standing waves are also important for large structures such as buildings and bridges. Superposition of light waves causes interference, which is used in electro-optic devices and precision measuring techniques.