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# 5. Wave Interference

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Lecture

In this mini-lecture, we introduce the concept of wave interference. As we move through this mini-lecture we consider: (i) constructive and destructive waves, pictorially and mathematically; (ii) examples of two-source interference in experiments, such as two laser sources sending out light waves and two hammers creating surface water waves; (iii) a mathematical analysis of two-source interference, which highlights the fact that the path difference x = dsinθ from the two sources to some point P results in complete constructive interference for angles θ associated with sinθ = nλ/d and complete destructive interference for angles θ associated with sinθ = (n + 1/2)λ/d, where d is the distance between the two sources, θ is the angle at which the wave travels to P, and n is some integer; (iv) the angle θ associated with the first null; and (v) laser interferometers used to detect gradational waves through the constructive interference of photons.

Course

In this course, Professor Steven Balbus (University of Oxford) explores waves. In the first mini-lecture, we introduce Hooke’s Law and solve for a mathematical solution that reveals the concept of Simple Harmonic Motion. In the second mini-lecture, we use a model of many masses on springs to understand properties of waves, including transverse and longitudinal waves, amplitude, wave number, wavelength, waves described in space and time, and wave velocity. The third mini-lecture discusses sound waves and water waves, including examples of sound waves in various mediums with various frequencies and tsunami waves. In the fourth mini-lecture, we give an overview of light waves and electromagnetic radiation. The fifth mini-lecture introduces constructive and destructive wave interference, as well as two-source interference. In the sixth mini-lecture, we turn towards diffraction, detailing Huygens' Construction used to determine the angles at which nulls in a wave appear in order to discuss a few examples with familiar objects. In the seventh mini-lecture, we introduce dispersive waves and go through two examples: surface water waves in deep water and waves such as FM radio waves passing through the Earth’s ionosphere. In the eighth mini-lecture, we briefly explore waves in modern physics, discussing Einstein’s photoelectric effect and the wave-like properties of particles, including photons (light particles).

Lecturer

Steven Balbus is the Savilian Professor of Astronomy at the University of Oxford and a Professorial Fellow at New College, Oxford. Before coming to Oxford, he was a Professeur des Universités in the Physics Department of the Ecole Normale Supérieure de Paris for nine years. He has also held academic positions at Princeton University, MIT, and the University of Virginia. Professor Balbus’ research interests lie in astrophysical fluid dynamics, particularly the behavior of magnetic gases. He has made distinguished contributions to our understanding of accretion disks, the dynamics of heating and cooling processes in hot plasmas, the behavior of gas in spiral galaxies, and the Sun’s internal rotation. In 2013, he was jointly awarded one of the highest honours in astronomy, the Shaw Prize, for his work on accretion disk turbulence, referred to as the magnetorotational instability. He received the Eddington Medal from the Royal Astronomical Society in 2020 and the Dirac Medal and Prize from the Institute of Physics (IoP) in 2021. Professor Balbus is a Fellow of the Royal Society and a member of the US National Academy of Sciences.

#### Cite this Lecture

APA style

Balbus, S. (2022, January 12). Waves - Wave Interference [Video]. MASSOLIT. https://massolit.io/courses/waves/wave-interference

MLA style

Balbus, S. "Waves – Wave Interference." MASSOLIT, uploaded by MASSOLIT, 12 Jan 2022, https://massolit.io/courses/waves/wave-interference