# Principle of Superposition Simulation

#### Quiz

When two waves overlap, the displacement of the medium is the sum of the displacements of the two individual waves. This is the principle of __________.

A. constructive interference
B. destructive interference
C. standing waves
D. superposition

The displacement due to two waves that pass through the same point in space is the algebraic sum of displacements of the two waves.

#### Principle of Superposition Simulation

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Interference of Waves
On the surface of a lake on a windy day, you will see many complicated wave motions (Figure 1). You will not see a simple wave moving in a particular direction. The water surface appears this way because of the action of many thousands of waves from various directions and with various amplitudes and wavelengths. When waves meet, a new wave is generated in a process called interference. In this section, you will learn what happens when two waves meet and interfere with each other.

Figure 1 The surface waves on this lake are the result of the interference of thousands of waves of different wavelengths and amplitudes. Most of these waves are caused by the wind, but they are also caused by passing boats and ships.

Wave Interference at the Particle Level
Waves are the result of particle vibrations, and that the particles in a medium are connected by forces that behave like small springs. Wave interference is influenced by the behaviour of the particles.
Wave motion is efficient: in most media, little energy is lost as waves move. When waves come together, this efficiency continues. When one wave passes in the vicinity of a particle, the particle moves up and down in an oval path, which allows the wave to move in a specific direction, as shown in Figure 2(a). When a second wave is also present, the vibration of the particle is modified. Th e oval motion of the particles stimulates the next particle in the direction of the wave’s motion to begin vibrating.
When two (or more) waves come together, as shown in Figure 2(b), the particle moves up and down rather than in an oval path because the speeds of the combined waves cancel each other out. Th e motion of the particle allows the waves to pass through each other. Th e waves are not modified, so the amount of energy stays the same. Th us, when two or more waves interact, the particle vibration is such that the direction and energy of each wave are preserved. Aft er the waves have passed through each other, none of their characteristics—wavelength, frequency, and amplitude—change.

Figure 2 (a) The basic motion of a vibrating particle in a travelling wave. (b) When two waves meet, the particle motion is more up and down. The wave characteristics are unchanged after the waves pass through each other.

Constructive and Destructive Interference
When two waves meet, the forces on their particles are added together. If the two waves are in phase (the phase shift between them is zero), then the resulting amplitude is the sum of the two original amplitudes. This is called the principle of superposition: the resulting amplitude of two interfering waves is the sum of the individual amplitudes.
Constructive interference occurs when two or more waves combine to form a wave with an amplitude greater than the amplitudes of the individual waves (Figure 3). Destructive interference occurs when two or more waves that are out of phase combine to form a wave with an amplitude less than at least one of the initial waves (Figure 4).

Figure 3 Constructive interference. Two wave pulses approach each other on a rope. Notice how the amplitudes of the two waves add together. Notice, also, how the waves are unchanged after they pass through each other. The amplitude during interference in (c) is the sum of the amplitudes of the two waves.

Figure 4 Destructive interference. When two wave pulses that are out of phase come together, the resulting amplitude is reduced.

Technology Using Interference of Waves
Noise-cancelling headphones, shown in Figure 5, use the concept of destructive interference. The electronics inside the headphones generate a wave that is out of phase with sound waves in the exterior environment. This out-of-phase wave is played inside the headset. Using destructive interference, the outside noise is cancelled.
Such devices allow users to listen to music at lower volume levels, reducing potential damage to their hearing.

Figure 5 A detector inside the headset determines what noise there is, and a speaker in the headphone emits the out-of-phase wave.