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Interference and superposition

Wave reflection at a boundary

Dan Russell’s tutorial on how waves reflect, when they hit a boundary.

Reflection from a hard boundary: Shake one end of a cord; the other end is fixed. A wave will travel down to the fixed end and be reflected back, inverted.

Relfection, when the wave is not tightly coupled to a wall. Here its tied to a string, which can slide on a pole.

Superposition

Superposition = what happens when one wave is superimposed – ‘placed on top’ – on another wave.

Superposition = algebraic sum of their separate displacements

Notice: Two waves pass through the same space, at the same time.

Waves are not bouncing off of each other – they pass through each other.

The result of superposition is called interference.

Constructive interference

Destructive interference

destructive-interference

A summary of the 2

wave-interference

Standing waves

What happens when two waves come at each other, at just the right speed and height?

A standing wave will be produced.

The resulting wave doesn’t move! It just goes up and down.

Here is a standing wave on a cymbal (from a drum set)
https://en.wikipedia.org/wiki/Standing_wave#/media/File:Drum_vibration_mode01.gif

Nodes and antinodes

NODES = points of destructive interference, where the object remains still

ANTINODES = points of constructive interference, where the object has maximum motion.

The nodes remain in fixed positions for a particular frequency.

Music and standing waves

Pluck a string on a guitar or violin.

Musicians call the first standing wave the fundamental, or first harmonic.

The higher frequency standing waves are callled overtones.

You can get overtones on many physical objects, like a cymbal, or any flat round disk.

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

PS4.A: Wave Properties

When a wave passes an object that is small compared with its wavelength, the wave is not much affected; for this reason, some things are too small to see with visible light, which is a wave phenomenon with a limited range of wavelengths corresponding to each color. When a wave meets the surface between two different materials or conditions (e.g., air to water), part of the wave is reflected at that surface and another part continues on, but at a different speed. The change of speed of the wave when passing from one medium to another can cause the wave to change direction or refract. These wave properties are used in many applications (e.g., lenses, seismic probing of Earth)… the wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. The reflection, refraction, and transmission of waves at an interface between two media can be modeled on the basis of these properties… At the surface between two media, like any wave, light can be reflected, refracted (its path bent), or absorbed. What occurs depends on properties of the surface and the wavelength of the light…. Lenses can be used to make eyeglasses, telescopes, or microscopes in order to extend what can be seen. The design of such instruments is based on understanding how the path of light bends at the surface of a lens.

 

 

 

 

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