Glossary

13.3 Wave Interaction: Superposition and Interference

3 min read•june 25, 2024

Wave and are fundamental concepts in physics that explain how waves interact. When multiple waves meet, they combine to form a new wave, creating fascinating phenomena like constructive and .

Understanding these principles is crucial for grasping more complex wave behaviors. From in musical instruments to interference patterns in light, wave superposition shapes our everyday experiences and underpins many technological applications.

Wave Superposition and Interference

Principle of wave superposition

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  • Wave superposition occurs when two or more waves interact and combine to form a resultant wave
    • Resultant wave is the sum of individual wave displacements at each point in space and time
    • Applies to all types of waves ( like sound and water, like light)
  • Effects of wave superposition on wave behavior
    • Leads to constructive or destructive interference
    • Changes of resultant wave (larger with , smaller with destructive interference)
    • Creates complex wave shapes like standing waves or
  • Wave superposition is described mathematically by the , which relates the wave's displacement to its position and time

Constructive vs destructive interference

  • Constructive interference
    • Occurs when waves with same and in (crests and troughs align) combine
    • Resulting wave has amplitude equal to sum of individual wave amplitudes
    • Examples: light forming bright fringes after passing through double slit, from in-phase speakers creating louder sound at certain locations
  • Destructive interference
    • Occurs when waves with same frequency and out of phase (crests align with troughs) combine
    • Resulting wave has amplitude equal to difference between individual wave amplitudes
    • In perfect destructive interference, waves completely cancel each other out
    • Examples: light forming dark fringes after passing through double slit, sound waves from out-of-phase speakers creating quieter sound or silence at certain locations
  • The between interfering waves determines the type and degree of interference

Formation of standing waves

  • Standing waves form by superposition of two waves with same frequency and amplitude traveling in opposite directions
    • Waves interfere to create pattern of (points of no displacement) and (points of maximum displacement)
    • Distance between adjacent nodes or antinodes is λ2\frac{\lambda}{2}, where λ\lambda is
  • Properties of standing waves
    • Stationary overall wave pattern that does not appear to move in space
    • Fixed locations of nodes and antinodes
    • Can form at specific frequencies called , which are integer multiples of
  • Formation of standing waves in various media
    • Strings: can form on string fixed at both ends (guitar string)
    • Air columns: can form in open or closed air columns (wind instruments like flute, clarinet)
    • Electromagnetic waves: can form in electromagnetic cavities (microwave ovens, laser cavities)

Wave Characteristics and Behavior

  • describes the displacement of a wave at any point in space and time
  • is the speed at which a wave propagates through a medium
  • refers to the degree of correlation between wave properties at different points in space or time, affecting interference patterns

Wave Reflection and Refraction

Wave reflection vs refraction

  • Wave
    • Change in direction of wave at interface between two media, causing wave to return to original medium
    • Caused by difference in properties of two media (density, stiffness)
    • equals
    • Applications: sound reflection (echoes), light reflection (mirrors), seismic wave reflection (geophysical exploration)
  • Wave
    • Change in direction of wave as it passes from one medium to another with different propagation speed
    • Caused by change in wave speed due to properties of new medium
    • related to angle of incidence by : sin⁡θ1v1=sin⁡θ2v2\frac{\sin \theta_1}{v_1} = \frac{\sin \theta_2}{v_2}
    • Applications: light refraction (lenses, prisms, optical fibers), sound refraction (underwater acoustics, atmospheric sound propagation), seismic wave refraction (geophysical exploration)

Key Terms to Review (32)

Amplitude: Amplitude is the maximum displacement or the maximum value of a periodic quantity, such as a wave or oscillation, from its equilibrium or mean position. It is a measure of the magnitude or size of a wave or vibration and is a fundamental property that describes the characteristics of various wave phenomena.
Angle of Incidence: The angle of incidence is the angle at which a wave, such as light or sound, strikes a surface. It is the angle between the incident wave and the normal (perpendicular) to the surface at the point of incidence. This term is crucial in understanding the behavior of waves as they interact with various media and surfaces.
Angle of Reflection: The angle of reflection is the angle at which a wave or particle is reflected off a surface. It is a fundamental concept in the study of wave interference and reflection, and is closely related to the angle of incidence.
Angle of Refraction: The angle of refraction is the angle at which a wave, such as light or sound, bends or changes direction when it passes from one medium to another with a different refractive index. This change in direction is a fundamental property of wave behavior known as refraction.
Antinodes: Antinodes are points along a medium where the amplitude of a standing wave is at its maximum. They occur at locations where the crests or troughs of two interfering waves constructively reinforce each other, resulting in a point of high displacement or pressure.
Beat Frequencies: Beat frequencies are the result of the interference between two waves of slightly different frequencies. When these waves combine, they create a new wave with a frequency that is the difference between the original frequencies, resulting in a periodic fluctuation in amplitude known as a beat.
Coherence: Coherence refers to the degree of correlation or consistency between different waves or parts of a wave. It is a crucial concept in the understanding of wave interactions, diffraction, and interference phenomena.
Constructive Interference: Constructive interference is a phenomenon that occurs when two or more waves of the same frequency and phase combine to produce a wave with a larger amplitude. This concept is fundamental to understanding the behavior of various types of waves, including sound waves, light waves, and electromagnetic waves.
Destructive Interference: Destructive interference occurs when two waves of the same frequency and amplitude, but opposite phase, combine to cancel each other out, resulting in a reduction or elimination of the wave amplitude at the point of interaction.
Electromagnetic Waves: Electromagnetic waves are a type of energy that travels through space and can be detected as electric and magnetic fields. They are a fundamental part of the electromagnetic spectrum and play a crucial role in various physical phenomena, including heat transfer, wave properties, and wave interactions.
Frequency: Frequency is a fundamental property of waves that describes the number of wave cycles that pass a given point in a unit of time. It is a measure of how often a wave oscillates or repeats itself and is a crucial parameter in understanding the behavior of various wave phenomena.
Fundamental Frequency: The fundamental frequency is the lowest frequency of a periodic waveform, such as a sound wave or an electrical signal. It is the frequency at which the waveform repeats itself and is the most prominent frequency component in the waveform's spectrum.
Harmonics: Harmonics refer to the natural vibrations or oscillations that occur at integer multiples of the fundamental frequency of a wave or system. These higher-frequency vibrations are superimposed on the primary wave, creating a complex waveform that is the sum of the fundamental and its harmonics.
Interference: Interference is the phenomenon that occurs when two or more waves interact with each other, resulting in the creation of a new wave pattern. This interaction can lead to either constructive interference, where the waves reinforce each other, or destructive interference, where the waves cancel each other out.
Light Waves: Light waves are a type of electromagnetic radiation that travels through space and can be perceived by the human eye. They are characterized by their wavelength, frequency, and energy, and play a crucial role in the phenomena of superposition and interference.
Mechanical Waves: Mechanical waves are disturbances that propagate through a medium, transferring energy without the permanent displacement of the medium itself. These waves are characterized by the vibration of the particles within the medium, which can be solids, liquids, or gases.
Nodes: Nodes are points along a wave where the amplitude or displacement of the wave is zero. They represent the locations where the wave interference results in complete destructive interference, causing the wave to cancel out entirely.
Phase: Phase refers to the relative position or state of a periodic phenomenon, such as a wave or a simple harmonic motion, at a given point in time. It describes the displacement of a waveform or the position of an oscillating object within its cycle.
Phase Difference: Phase difference refers to the difference in the phase or position of two waves or oscillations within a periodic system. It describes the relative timing or displacement between two wave signals, which is a crucial concept in understanding the behavior of waves, particularly in the context of superposition, interference, and diffraction.
Reflection: Reflection is the change in direction of a wave, such as light or sound, when it encounters a boundary or surface. It is a fundamental concept in the study of wave phenomena and plays a crucial role in various fields, including optics, acoustics, and the understanding of the electromagnetic spectrum.
Refraction: Refraction is the bending of waves, such as light or sound, when they pass from one medium to another with a different density or refractive index. This change in direction occurs due to the difference in the speed of the wave as it moves through the two mediums.
Seismic Waves: Seismic waves are the waves of energy that travel through the Earth's interior or along its surface following an earthquake or other seismic event. These waves are crucial in understanding the structure and composition of the Earth, as well as in detecting and monitoring seismic activity.
Snell's Law: Snell's law is a fundamental principle in optics that describes the relationship between the angles of incidence and refraction when light passes from one medium to another with different refractive indices. It is a critical concept in understanding the behavior of electromagnetic radiation, reflection, refraction, and the functioning of lenses.
Sound Waves: Sound waves are mechanical vibrations that propagate through a medium, such as air or water, and can be detected by the human ear. These waves are characterized by their ability to carry energy and information, and they are essential in various fields, including physics, acoustics, and communication.
Standing Waves: Standing waves are a pattern of wave interference that occurs when waves of the same frequency reflect back on themselves, creating regions of constructive and destructive interference. This phenomenon is observed in various wave-based systems, including sound and electromagnetic waves.
Superposition: Superposition is the principle that when two or more waves interact, the resulting wave pattern is the sum of the individual wave patterns. This concept applies to various types of waves, including sound waves, electromagnetic waves, and waves in physical media such as water and air.
Water Waves: Water waves are periodic disturbances that propagate through a body of water, such as an ocean, lake, or river. These waves are created by the oscillation of water particles, which transfer energy through the medium without the actual movement of the water itself.
Wave Displacement: Wave displacement refers to the distance a point on a wave has moved from its equilibrium or resting position. It describes the vertical movement or oscillation of a wave as it propagates through a medium, such as air, water, or a solid material.
Wave Equation: The wave equation is a fundamental mathematical equation that describes the propagation of waves, such as sound waves, water waves, and electromagnetic waves, through a medium or in a vacuum. It is a partial differential equation that relates the displacement or amplitude of a wave to its spatial and temporal coordinates.
Wave Function: The wave function is a mathematical description of the quantum state of an object or particle. It provides a complete description of the particle's behavior and evolution over time, and its square gives the probability density of the particle's position in space.
Wave Velocity: Wave velocity is the speed at which a wave propagates or travels through a medium. It is a fundamental property of waves that describes how quickly the disturbance or oscillation moves through the medium, independent of the motion of the medium itself.
Wavelength: Wavelength is a fundamental characteristic of waves, referring to the distance between consecutive peaks or troughs of a wave. It is a crucial parameter that, along with frequency and speed, defines the properties and behavior of various wave phenomena in physics.
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