Waves Physics Lesson 16 by Owen Borville 12.9.2025
Wave are disturbances or natural phenomenon that move from the initial point with a wave velocity vw.
Wavelength λ is the distance between adjacent identical parts of the wave.
Wave velocity and wavelength are related to the wave's frequency and period by vw = λ/T or vw = ƒλ
Mechanical waves are disturbances that move through a medium and follow Newton's laws.
Electromagnetic waves are disturbances in the electric and magnetic fields and do not require a medium.
Matter waves are an important part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
Transverse waves have disturbances perpendicular to their direction of propagation, whereas longitudinal waves have disturbances parallel to their direction of propagation.
Superposition is the combination of two waves at the same location.
Constructive interference occurs when two identical waves are superimposed in phase.
Destructive interference occurs when two identical waves are superimposed exactly out of phase.
A standing wave is one in which two waves superimpose to produce a wave that varies in amplitude but does not propagate.
Nodes are points of no motion in standing waves.
An antinode is the location of maximum amplitude of a standing wave.
Waves on a string are resonant standing waves with a fundamental frequency and can occur at higher multiples of the fundamental, called overtones or harmonics.
Beats occur when waves of similar frequencies f1 and f2 are superimposed. The resulting amplitude oscillates with a beat frequency given by fB = |f1-f2|
Intensity is the power per unit area: I = P/A and has units of W/m^2
A wave is an oscillation of a physical quantity that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both up and down and back and forth, around an equilibrium position.
A snapshot of a sinusoidal wave at time t = 0.00 s can be modelled as a function of position. Two examples of this are y(x) = Asin(kx + φ) and y(x) = Acos(kx + φ)
Motion of a pulse or wave moving at constant velocity can be modelled with a function of a wave that is a snapshot of the wave, and is only a function of the position x. The x is replaced with (x +/- vt). The minus sign is for motion in the positive direction and the plus sign is for motion in the negative direction.
The wave function is y (x, t) = A sin(kx-ωt+φ) where k = 2π/λ is defined as the wave number, ω = 2π/Τ is the angular frequency, and φ is the phase shift.
Phase of a wave = kx +/- ωt + φ
The wave moves with constant velocity vw, where the particles of the medium oscillate about an equilibrium position. The constant velocity of a wave can be found by v = λ/T = ω/k
The speed of a wave on a string depends on the linear density of the string and the tension in the string. The linear density is mass per unit length of the string.
Generally the speed of a wave depends on the square root of the ratio of the elastic property to the inertial property of the medium.
The speed of a wave through a fluid is equal to the square root of the ratio of the bulk modulus of the fluid to the density of the fluid.
The speed of sound through the air at T = 20 degrees C is about vs = 343.00 m/s.
The energy and power of a wave are proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave.
Time-averaged power of a sinusoidal wave on a string is found by Pave = Eλ/T = 1/2μA^2ω^2v, where μ is the linear mass density of the string, A is the amplitude of the wave, ω is the angular frequency of the wave, and v is the speed of the wave.
Intensity is the power divided by the area (I = P/A). In a spherical wave, the area is A = 4πr^2 and the intensity is I = P/4πr^2. As the wave moves out from a source, the energy is conserved, but the intensity decreases as the area increases.
Superposition is the combination of two waves at the same location. Constructive interference occurs from the superposition of two identical waves that are in phase. Destructive interference occurs from the superposition of two identical waves that are 180 degrees (π radians) out of phase.
The wave that results from the superposition of two sine waves that differ only by a phase shift is a wave with an amplitude that depends on the value of the phase difference.
A standing wave is the superposition of two waves which produces a wave that varies in amplitude but does not propagate. Nodes are points of no motion in standing waves. An antinode is the location of maximum amplitude of a standing wave.
The equation of a standing wave is y (x, t) = [2Asin(kx)]cos( ωt)
Normal modes of a wave on a string are the possible standing wave patterns. Fundamental frequency is the lowest frequency that will produce a standing wave. Overtones are the higher frequencies that produce standing waves.
Linear mass density = μ = mass of string/length of string = m/l
Speed of a wave or pulse on a string under tension = |v| = √FT/μ
Speed of a compression wave in a fluid = v = √B/ρ
Wave number = k = 2π/λ
Wave speed = v = ω/k
Wavelength for symmetric boundary conditions = λn = 2/nL, n = 1, 2, 3, 4, 5 ...
Frequency for symmetric boundary conditions = ƒn = nv/2L = nf1, n = 1, 2, 3, 4, 5 ...
Wave are disturbances or natural phenomenon that move from the initial point with a wave velocity vw.
Wavelength λ is the distance between adjacent identical parts of the wave.
Wave velocity and wavelength are related to the wave's frequency and period by vw = λ/T or vw = ƒλ
Mechanical waves are disturbances that move through a medium and follow Newton's laws.
Electromagnetic waves are disturbances in the electric and magnetic fields and do not require a medium.
Matter waves are an important part of quantum mechanics and are associated with protons, electrons, neutrons, and other fundamental particles found in nature.
Transverse waves have disturbances perpendicular to their direction of propagation, whereas longitudinal waves have disturbances parallel to their direction of propagation.
Superposition is the combination of two waves at the same location.
Constructive interference occurs when two identical waves are superimposed in phase.
Destructive interference occurs when two identical waves are superimposed exactly out of phase.
A standing wave is one in which two waves superimpose to produce a wave that varies in amplitude but does not propagate.
Nodes are points of no motion in standing waves.
An antinode is the location of maximum amplitude of a standing wave.
Waves on a string are resonant standing waves with a fundamental frequency and can occur at higher multiples of the fundamental, called overtones or harmonics.
Beats occur when waves of similar frequencies f1 and f2 are superimposed. The resulting amplitude oscillates with a beat frequency given by fB = |f1-f2|
Intensity is the power per unit area: I = P/A and has units of W/m^2
A wave is an oscillation of a physical quantity that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both up and down and back and forth, around an equilibrium position.
A snapshot of a sinusoidal wave at time t = 0.00 s can be modelled as a function of position. Two examples of this are y(x) = Asin(kx + φ) and y(x) = Acos(kx + φ)
Motion of a pulse or wave moving at constant velocity can be modelled with a function of a wave that is a snapshot of the wave, and is only a function of the position x. The x is replaced with (x +/- vt). The minus sign is for motion in the positive direction and the plus sign is for motion in the negative direction.
The wave function is y (x, t) = A sin(kx-ωt+φ) where k = 2π/λ is defined as the wave number, ω = 2π/Τ is the angular frequency, and φ is the phase shift.
Phase of a wave = kx +/- ωt + φ
The wave moves with constant velocity vw, where the particles of the medium oscillate about an equilibrium position. The constant velocity of a wave can be found by v = λ/T = ω/k
The speed of a wave on a string depends on the linear density of the string and the tension in the string. The linear density is mass per unit length of the string.
Generally the speed of a wave depends on the square root of the ratio of the elastic property to the inertial property of the medium.
The speed of a wave through a fluid is equal to the square root of the ratio of the bulk modulus of the fluid to the density of the fluid.
The speed of sound through the air at T = 20 degrees C is about vs = 343.00 m/s.
The energy and power of a wave are proportional to the square of the amplitude of the wave and the square of the angular frequency of the wave.
Time-averaged power of a sinusoidal wave on a string is found by Pave = Eλ/T = 1/2μA^2ω^2v, where μ is the linear mass density of the string, A is the amplitude of the wave, ω is the angular frequency of the wave, and v is the speed of the wave.
Intensity is the power divided by the area (I = P/A). In a spherical wave, the area is A = 4πr^2 and the intensity is I = P/4πr^2. As the wave moves out from a source, the energy is conserved, but the intensity decreases as the area increases.
Superposition is the combination of two waves at the same location. Constructive interference occurs from the superposition of two identical waves that are in phase. Destructive interference occurs from the superposition of two identical waves that are 180 degrees (π radians) out of phase.
The wave that results from the superposition of two sine waves that differ only by a phase shift is a wave with an amplitude that depends on the value of the phase difference.
A standing wave is the superposition of two waves which produces a wave that varies in amplitude but does not propagate. Nodes are points of no motion in standing waves. An antinode is the location of maximum amplitude of a standing wave.
The equation of a standing wave is y (x, t) = [2Asin(kx)]cos( ωt)
Normal modes of a wave on a string are the possible standing wave patterns. Fundamental frequency is the lowest frequency that will produce a standing wave. Overtones are the higher frequencies that produce standing waves.
Linear mass density = μ = mass of string/length of string = m/l
Speed of a wave or pulse on a string under tension = |v| = √FT/μ
Speed of a compression wave in a fluid = v = √B/ρ
Wave number = k = 2π/λ
Wave speed = v = ω/k
Wavelength for symmetric boundary conditions = λn = 2/nL, n = 1, 2, 3, 4, 5 ...
Frequency for symmetric boundary conditions = ƒn = nv/2L = nf1, n = 1, 2, 3, 4, 5 ...