Interference

# 32 Interference: Overview

Experience with sound suggests that waves don’t collide like particles do. When two people talk simultaneously during a conversation, each person hears both people- not just themselves. This simple observation suggests two important properties of not just sound, but all waves. First, waves (sound or otherwise) from different sources can (and do) pass through each other. Second, waves from multiple sources can co-exist at the same location at the same time.

This chapter explores what happens when waves overlap. When waves overlap, the individual waves add together to form a single wave. The math is addition. The central idea is called the principle of superposition:

At all locations where two (or more) waves (or pulses) overlap, the displacement of the resulting wave (or pulse) is equal to the sum of the displacements each wave (or pulse) would have if it was at the location alone.

Most of the time, superposition leads to the results you expect. When two people are talking at you at the same time, what you hear is both people at once. When you hear two instruments play two notes together, you usually hear two notes playing together.

However, the results of superposition can sometimes be very surprising. The height of a wave at any location can be either “positive” or “negative,” so when waves occupy the same location, they can up to zero! In other words, sounds can “cancel each other out” and at any moment and at any location. Most of the time, the cancellation is temporary and has no practical effect on the sound. However, depending on the types of sounds and how the sound waves line up, superposition can lead to interesting and noticeable effects.

### Interference: Learning Objectives

• Explain how the principle of superposition applies to waves
• Define interference, constructive interference, destructive interference, beats, beat frequency, difference tone
• Apply the principle of superposition
• Explain these phenomena using the principle of superposition:
• beats
• standing waves
• reflection
• nodal (and antinodal) lines
• Determine whether two sources will constructively (or destructively interfere) at any given location