Name: interference from different path lengths
Uploaded: 2023-05-16T08:18:41.000Z
Duration: 1 min 10 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

NC K-12 Science Standard Course of Study

9-12

Physical Science

Waves and Their Applications

PS.PSc.8.3

Interference: Path Lengths

Imaginez que deux haut-parleurs soient alimentés par la même source sonore d’une seule fréquence. Dans ce cas, les deux ondes n’ont pas de différence de phase au niveau des haut-parleurs.
Rappelez-vous que les ondes sonores sont des ondes progressives impliquant à la fois des coordonnées spatiales et temporelles. Ainsi, en un point P, la distance parcourue par les deux ondes diffère.
Les ondes s’expriment en termes de chemins parcourus. Une différence de phase a été introduite simplement en raison de la différence de longueur de trajet, appelée différence de trajet.
Si la différence de trajet est un multiple intégral de la longueur d’onde, les ondes interfèrent de manière constructive. S’il s’agit d’un multiple intégral de la demi-longueur d’onde, ils interfèrent de manière destructrice. Pour cette raison, lorsque deux crêtes ou deux auges se rencontrent, elles interfèrent de manière constructive, tandis que les crêtes et les auges interfèrent de manière destructrice.
En d’autres points que les crêtes et les creux, l’amplitude est intermédiaire.
Si les haut-parleurs étaient alimentés par différentes sources avec une différence de phase fluctuante, le motif d’interférence changerait rapidement et serait effacé.

<ol>
	<li>Young, H.D et Freedman, R.A. (2012). La physique universitaire avec la physique moderne. San Francisco, Californie : Pearson : article 16.6 ; Pages 529 et 530.</li>
	<li>OpenStax. (2019). Physique universitaire Vol. 1. [Version Web]. Extrait de <a href="https://openstax.org/books/university-physics-volume-1/pages/1-introduction">https://openstax.org/books/university-physics-volume-1/pages/1-introduction :</a> section 17.4 ; Pages 869 à 871.</li>
	<li>Verma, H.C. (2008). Concepts de physique. Volume 1, Bharati Bhawan Pub. & Dis. ; l’article 16.8 ; Pages 335 et 336.</li>
</ol>

interférence : longueurs de chemin

Considérez deux sources de son, qui peuvent être en phase ou non, émettant des ondes à une fréquence unique, et considérez que les fréquences sont les mêmes.
Deux sources spéciales peuvent être considérées lorsqu'elles sont en phase. Cela peut être facilement accompli en alimentant les deux sources à partir de la même source. Un exemple serait de synchroniser les deux haut-parleurs en les alimentant avec la même source, comme les ondes sonores produites par un diapason. Cette configuration garantit que les deux sources ont la même fréquence et sont en phase au départ. Elles provoquent ensuite une interférence dans la région environnante.

Cependant, les ondes parcourent des chemins différents vers des points différents, et en général, les longueurs de chemin sont différentes. Rappelant que les ondes sonores, ou toute onde se déplaçant, dépendent à la fois des coordonnées spatiales et temporelles, il est facile de voir que la différence de longueurs de chemin entraîne une différence de phase dans les ondes à différents points. Le motif d'interférence est affecté par la différence de chemin.

Cette configuration explique explicitement que l'interférence est causée non seulement par les différences de phase dues à la différence de phase initiale ou à la différence de fréquences, mais aussi par la différence de longueurs de chemin. Cela a des implications importantes pour les ondes lumineuses.

Notez cependant que la différence de chemin affecterait le motif d'interférence même si les deux sources ont une différence de phase de départ constante. Si les deux sources n'ont pas une différence de phase de départ constante, mais que la différence de phase fluctue rapidement, alors l'interférence fluctuerait rapidement entre constructive et destructive à tous les points. L'intensité changerait également rapidement entre le maximum et le minimum à tous les points. Les oreilles humaines ne perçoivent pas les changements rapides d'intensité et perçoivent l'effet moyen, qui est simplement la somme des intensités des deux sources.

Interférence : Longueurs de chemin

Considérons deux sources de son, qui peuvent être en phase ou non, émettant des ondes à une seule fréquence, et considérez que les fréquences sont identiques.
Deux...

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Education

Enseignement

JoVE Core

Physics

Physique

Unit 1

Unité 1

Sound

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

interference from different path lengths

Interference from different path lengths explains how two sound sources can create changing patterns in space. The sources may or may not start in phase, but they emit waves at the same frequency. When they are in phase, they are called coherent sources, and that is easy to arrange by feeding both speakers from the same source, such as a tuning fork.

These synchronized sources start with the same frequency and the same phase. As the waves move outward, they travel different distances to reach different points. That difference in path length creates a phase difference at each point, so the interference pattern changes from place to place.

This idea shows that interference is not caused only by an initial phase difference or by different frequencies. Path difference also changes the pattern, even when the two sources keep a constant starting phase difference. The same principle matters for light waves as well.

If the phase difference between the two sources does not stay constant and instead changes rapidly, the interference also shifts quickly between constructive and destructive at every point. The intensity then moves rapidly between its maximum and minimum values. Human ears do not notice these fast changes well, so they hear the average effect, which is simply the sum of the two source intensities.

Interference from Different Path Lengths

sound waves

How Sound Travels Through Matter

Sound travels through matter as pressure changes in a medium. These changes make the particles of the medium move back and forth around their mean position. Sound can also be modeled as particle displacement as the wave passes through air, water, or another material. In most fluids, sound waves are longitudinal waves. That means the particles vibrate in the same direction that the wave moves. Fluids do not support lateral pressure well, so sound in liquids and gases mainly moves this way. <br...

sound as pressure waves

Sound Pressure in Longitudinal Waves

Sound waves are longitudinal waves that create changing pressure in a medium. Their displacement amplitude can be modeled as a function of position and time. As one column of the medium moves, nearby columns also move. The difference between these successive displacements produces a pressure change compared with the surrounding pressure. This pressure change is called gauge pressure. It varies across the medium because the pressure fluctuation depends on how much one point is displaced...

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perception of sound waves

How Ear Sensitivity Shapes Sound

The human ear does not respond the same way to every sound frequency. Sounds with the same pressure can seem louder or softer when their frequencies change. Ear health also affects this perception, and hearing can decline with age. Regular exposure to loud noises may also damage the ears over time. Pitch depends on both frequency and pressure amplitude, which is the size of the sound wave’s pressure change. Two sounds with the same frequency and pressure amplitude have the same pitch. If the...

speed of sound in solids and liquids

Why Sound Moves Faster in Dense Materials

Sound moves faster in solids and liquids because their particles are close together and can pass along disturbances quickly. Most solids and liquids are incompressible, which means their densities stay nearly constant throughout. When an external force acts on them, the molecules try to return to their original positions. That restoring motion happens because the particles interact with one another. These interactions let sound waves carry information through the material. As a result, sound...

speed of sound in gases

What Changes Sound Speed in Gases?

Sound speed in gases depends on gas properties, pressure, volume, and temperature. Gas molecules move freely, so gases are highly compressible. Because of that compressibility, sound waves travel more slowly through gases than through many other media. The speed of sound in an ideal gas can be found using thermodynamics. Thermodynamics links pressure, volume, and temperature, which helps describe how sound moves through a gas. Newton's laws of motion and the continuity equation from fluid...

deriving the speed of sound in a liquid

Sound Speed in Fluids: Bulk Modulus

Sound speed in fluids depends on a fluid’s bulk modulus and density. These two properties describe how stiff the fluid is and how much inertia it has. For mechanical waves in a fluid, that relationship follows the same pattern used for Young’s modulus and density in solids. The speed of sound in a liquid can be derived by treating the wave as a longitudinal wave moving through the medium. The derivation uses the gauge pressure expression and the impulse-momentum theorem. This same result...

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sound intensity

Measuring How Loud Sound Is

Sound intensity helps describe how loud a sound source is. It depends on how energetically the source vibrates, because those vibrations make the molecules in the medium vibrate as well. Intensity is the energy emitted per unit time per unit area. The area must be perpendicular to the direction the sound wave travels. Using time and area makes the measure reflect the source’s own loudness, even when the source vibrates over a longer time or spreads energy over a larger area. A sound source...

sound intensity level

Measuring Sound with Decibels

Sound intensity level helps measure how loud sound is. The human ear sends sound waves to the brain, and the brain turns those waves into hearing. The loudness of the surrounding environment affects whether a person can tell different sound sources apart. The ear can detect a very wide range of sound intensity. Because of that range, scientists use a logarithmic scale to describe intensity level. Intensity level is a ratio of two intensities, so it has no unit. The standard reference is the...

intensity and pressure of sound waves

Sound Intensity from Displacement and Pressure

Sound intensity can be linked to displacement and pressure in a wave. The key idea is to use the wave expressions and the definition of intensity. To do that, the power carried by the particles is written as force times velocity, and the force per unit area is treated as pressure. The particle velocity can be found from the displacement of the medium. A sinusoidal term averages to zero over time because it is positive and negative for equal parts of each cycle. Its square does not average to...

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sound waves: interference

Sound Wave Interference in Speakers

Sound wave interference can change the loudness of sound when two waves meet. Sound waves may be modeled as longitudinal waves, where molecules move around an equilibrium position, or as pressure waves. When two identical waves from the same source overlap, their crests or troughs can add together. This is called constructive interference, and it increases amplitude. If identical waves start in phase but travel different path lengths, they can become out of phase. Then a crest can meet a...

interference: path lengths

Interference from different path lengths explains how two sound sources can create changing patterns in space. The sources may or may not start in phase, but they emit waves at the same frequency. When they are in phase, they are called coherent sources, and that is easy to arrange by feeding both speakers from the same source, such as a tuning fork. These synchronized sources start with the same frequency and the same phase. As the waves move outward, they travel different distances to reach...

sound waves: resonance

Sound Waves in Tubes and Strings

Sound waves can form resonance patterns in strings and tubes when the boundary conditions match the wave frequency. On a string under tension, symmetrical boundary conditions create a node at each end. A node is a fixed point where the string does not move. Some frequencies then produce standing waves, while other frequencies interfere destructively. Resonance also appears in a hollow tube. In a tube closed at one end and open at the other, a vibrating tuning fork near the open end sends an...

beats

Sound Interference and Beats

Sound interference creates beats when two or more close frequencies combine. In music, this shows up as a changing loudness that rises and falls. The pattern comes from superposition, the adding together of waves. Constructive interference makes the sound stronger, while destructive interference makes it weaker. Music usually contains many changing frequencies from instruments and voices. A single sound at one frequency for a long time can feel dull or even irritating. It can sound like the...

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doppler effect - i

Doppler Shift in Sound and Light

The Doppler effect describes how the frequency of a wave changes when the source and the observer move relative to each other. It was named after the Austrian physicist and mathematician Christian Johann Doppler in 1842. He studied both moving sources and moving observers. A simple example is an ambulance passing a person standing on a street corner. As the ambulance approaches, the siren seems louder. As it moves away, the sound gets quieter. The pitch also changes. The high siren sound...

doppler effect - ii

Doppler Radar and Heart Blood Flow

Doppler effect applications appear in weather forecasting and medical imaging. In these uses, a change in frequency helps show motion. The reflected signal can reveal whether an object is moving toward or away from the source. Meteorologists use Doppler radar to study weather events. A transmitter sends radio waves at a set frequency toward the sky from a weather station. The waves bounce off clouds and precipitation and return to the station. If the reflected radio frequency decreases, the...

shock waves

Sonic Booms and Supersonic Motion

Sonic booms and supersonic motion happen when a sound source moves as fast as, or faster than, sound in the medium. In the Doppler formula for sound, it is usually assumed that sound travels faster than the source. When that assumption fails, a shock wave can form. As the source gets close to the speed of sound, successive wavefronts build up by constructive interference right behind it. Scientists once thought this pressure buildup would keep an airplane from breaking the sound barrier and...

echo

Echo Sound and Distance Detection

Echo is a reflected sound that returns after the original sound has been heard. The human ear cannot tell two sounds apart if they arrive within about 0.1 seconds of each other. When the reflected sound takes longer than that to return, the ear hears two separate sounds instead of one. This effect is easy to notice when the sound source is close to a surface that sends the sound back. If the sound and its reflection are separated by enough time, the result is an echo. A minimum distance of...

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key terms and concepts

Learn how sound waves from in-phase speakers create interference when different path lengths produce phase differences, and why this also matters for light.

Interference from Different Path Lengths | JoVE K12

physics

JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

Pennsylvania State Academic Standards

Waves and Electromagnetic Radiation

3.2.9-12.V

Louisiana Student Standards for Science

High School

waves-and-their-applications-in-technologies-for-information-transfer

Waves And Their Applications In Technologies For Information Transfer

HS-PS4-1

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Energy And Waves

Waves

Wave properties

Tennessee Academic Standards

Waves and Their Applications in Technologies for Information Transfer

PHYS.PS4.4

PHYS.PS4.6

PHYS.PS4.7

Virginia  Standards of Learning

HIgh School

PS.6

PS.6.c

PH.5

PH.5.b

Alabama Course of Study Science

9-12.PS.2.2.e

9-12.P.3.7.b

Next Generation Science Standards

HS-PS4-3

Texas Essential Knowledge and Skills

PHYS.8

PHYS.8.D

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Waves and Electromagnetic Radiation

HS-PS4-3.

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PS.PSc.8.1

Electromagnetic Waves

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Electromagnetic Wave Equation

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Use models to compare the characteristics of mechanical and electromagnetic waves.

PS.PSc.8.2

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Reflection of Waves

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Propagation of Waves

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Sound Waves: Interference

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Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two ...

Use models to explain the wave interactions of reflection, refraction, diffraction, and interference.

Standing Waves

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Modes of Standing Waves - I

A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. ...

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Modes of Standing Waves: II

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions ...

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Obtain, evaluate, and communicate information to explain how instruments that transmit and detect waves are used in everyday life.

PS.PSc.8.4

Analyze the nature of waves and their applications.

Interference from Different Path Lengths

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