IB PHYSICS Topic 4: Oscillations and Waves

__4.1 Oscillations__

__4.1 Oscillations__

**Periodic Motion:**Motion that repeats itself after equal intervals of time.

Examples include the motion of a loaded spring, an object moving in a circle, and a simple pendulum.

**Terms Related to Periodic Motion:****Amplitude (A):**Maximum displacement from the equilibrium position.**Time period (T):**Time taken for a complete oscillation.**Frequency (f):**Number of oscillations per unit time. (f = 1/T)**Angular frequency (𝓌):**Equivalent of frequency. (𝓌 = 2(π)f)**Phase (θ):**If the motion starts away from equilibrium, it leads or lags by θ.**Isochronous oscillations:**Maintain a constant time period regardless of amplitude changes.

**Simple Harmonic Motion (SHM):**A type of periodic motion where the restoring force is proportional to the negative displacement from the equilibrium position.

Examples include a spring-loaded with a mass and a simple pendulum with a small amplitude.

Equation defining SHM: a - kx where a is accelerated, k is a constant, and x is displacement.

**Units of constant k:**K = - a/x, so the unit of k is m x s^-2 / m = s^-2

**.**

**Difference in oscillations of two systems S1 and S2.**If S1 has frequency f, S2 with 4k frequency has a frequency of √4f = 2f

**Describing Simple Harmonic Motion:**Equation for SHM

**: x = Asin(2πft + θ) = Asin(wt + θ),**where θ is π/2

**Velocity (v):**v = (dx)/(dt) = 𝓌Acos(𝓌t + θ)

**Acceleration(a):**a = (dv)/(dt) = -𝓌^2(A)(sin(𝓌t+θ))

**Phase difference between displacement-time graphs:**About 25 seconds

0.79 radians

**Circular Motion and SHM:**The projection of an object in circular motion on a diameter follows simple harmonic motion.

**Energy Changes in Simple Harmonic Motion:****Kinetic energy**: KE= ½(m𝓌^2A^2)Total energy remains constant in the absence of dissipative forces.

**Waves and their types:****Mechanical waves:**require a material medium to travel**Electromagnetic waves:**can travel through a vacuum.

**Describing Waves:****Wavefront:**A surface perpendicular to the direction of wave travel.**Amplitude (A):**Maximum displacement from equilibrium.**Wavelength (⅄):**Shortest distance between two points in phase on a wave.**Period (T):**Time for a complete wavelength to pass a fixed point.**Frequency (f):**Number of wavelengths passing through a fixed point per unit time.f = 1/T

__4.2 Traveling waves__

__4.2 Traveling waves__

**Transverse waves:**Direction of vibration perpendicular to the direction of propagation.**Longitudinal waves:**Direction of vibration parallel to the direction of propagation.**Wave Equation:**The velocity of a wave (c) is given by c = f⅄

**Electromagnetic waves:**Travel with varying electric and magnetic fields at 3 x 10^8 m/s in a vacuum.

__4.3 Wave characteristics__

__4.3 Wave characteristics__

**Intensity of Waves:**Intensity (I) is power received per unit area. I = (P)/(4πr^2) and is proportional to the square of amplitude (A^2).

Example:

Intensity at 120m from source: 3 x 10^-6 W/m^2.

**Principle of Superposition:**When two waves meet, the total displacement is the vector sum of their individual displacements.

**Polarization:**Restriction of oscillation direction to a plane perpendicular to the direction of propagation. Result: Plane-polarized light.

**Malus’s Law:**Intensity (I) transmitted by an analyzer is proportional to cos^2(θ) where θ is the angle between the polarizer and the analyzer.

__4.4 Wave Behaviour__

__4.4 Wave Behaviour__

**Laws Of Reflection And Refraction:**Incident, reflected, and refracted rays, and normal lie on the same plane.

The angle of incidence equals the angle of reflection.

*(sinθ1)/(sinθ2) = 1/n*(Snell’s Law)

**Reversibility of Light:***(sinθ1)/(sinθ2) = 1/n_2*for light going from medium 1 to medium 2, and*(sinθ1)/(sinθ2) = 1/n_1*for light traveling in the opposite direction.

**Critical Angle And Total Internal Reflection:**The angle of incidence for which the angle of refraction reaches the right angle is the critical angle.

Total internal reflection occurs when the angle of incidence is greater than the critical angle.

**Double-Slit Interference:**Two coherent sources create interference patterns. Constructive interference occurs at nλ and is destructive at (n + ½)λ.

**Example:**The path difference at point P is 7λ. The nature of the fringe at P is bright, and there are 7 dark fringes between O and P.

**Diffraction:**Wave passed through a narrow gap forms bright and dark fringes. Angular position of minima given by θ = (nλ/a).

**Example:**Path difference at point P is 7λ.

The nature of fringe at P is bright, and there are 7 dark fringes between O and P.

**Interference With Multiple Slits:**More slits result in sharper and more intense maxima and minima.

**Dispersion:**Different wavelengths of light refract at different angles. White light disperses into its constituent wavelengths.

**Resolution:**Rayleigh's criterion states two points are just resolved if the central maximum of the first point falls on the first minimum of the second point.

**Diffraction Grating:**For a grating with N slits, R = λ/change in λ = mN

**Reflection Of Light Off Thin Films:**Reflected light undergoes a phase change of 180∘ if reflected off a denser medium.

A thin film of thickness t, refractive index n, and incident wavelength λ exhibits interference.

**Doppler Effect In Light:**The change in frequency of the light wave is (v/c)(f_0).

**Water Waves:**Follow laws similar to light. Exhibit reflection, refraction, interference, and diffraction.

**Wave Propagation:**Wavefront consists of infinite new disturbance centers.

Successive wavefronts result from wavelets from these disturbances.

**Reflection Of Water Wave:**When a wave hits a barrier, it behaves as if a similar wave is coming from the barrier in the opposite direction.

**Doppler Effect In Sound:**The frequency of a moving source changes for an observer at rest or moving toward/away from the source.

__4.5 Standing waves__

__4.5 Standing waves__

**Boundary Conditions:**Reflected off a fixed boundary suffers a phase change of 180∘.

No change in the phase of a free boundary.

**Standing Waves:**Formed when two waves of equal amplitude and frequency traveling in opposite directions are superimposed.

Positions of crests and troughs do not change with time.

**Nodes and Antinodes:**Nodes are points with zero displacement, antinodes are points with maximum displacement.

**Harmonics On A String:**The string is tied at one end and connected to a vibration generator at the other.

Harmonics formed with increasing loops at

*n*times the frequency of the first harmonic.

**Displacement of string at different times:**Quarter of a cycle: t = 1/4f

Half of a cycle: t = 1/2f

**Frequency of vibration of the spring:**Wavelength 2L, wave velocity 240 m/s, frequency 120 Hz.

**Harmonics In A Pipe:**Harmonics formed with one end open or both ends open. Nodes form at closed ends and antinodes at open ends.

**Explanation regarding refraction of light:**The speed of light is faster in a vacuum than in water, bending away from normal.

**The critical angle for total internal reflection:**sinፀ_c = 1/n

where

*n*is the relative refractive index of denser material with respect to rarer material.

**Frequency of the first harmonic if both ends are open:**Twice the frequency of the first harmonic when one end is closed

# IB PHYSICS Topic 4: Oscillations and Waves

__4.1 Oscillations__

__4.1 Oscillations__

**Periodic Motion:**Motion that repeats itself after equal intervals of time.

Examples include the motion of a loaded spring, an object moving in a circle, and a simple pendulum.

**Terms Related to Periodic Motion:****Amplitude (A):**Maximum displacement from the equilibrium position.**Time period (T):**Time taken for a complete oscillation.**Frequency (f):**Number of oscillations per unit time. (f = 1/T)**Angular frequency (𝓌):**Equivalent of frequency. (𝓌 = 2(π)f)**Phase (θ):**If the motion starts away from equilibrium, it leads or lags by θ.**Isochronous oscillations:**Maintain a constant time period regardless of amplitude changes.

**Simple Harmonic Motion (SHM):**A type of periodic motion where the restoring force is proportional to the negative displacement from the equilibrium position.

Examples include a spring-loaded with a mass and a simple pendulum with a small amplitude.

Equation defining SHM: a - kx where a is accelerated, k is a constant, and x is displacement.

**Units of constant k:**K = - a/x, so the unit of k is m x s^-2 / m = s^-2

**.**

**Difference in oscillations of two systems S1 and S2.**If S1 has frequency f, S2 with 4k frequency has a frequency of √4f = 2f

**Describing Simple Harmonic Motion:**Equation for SHM

**: x = Asin(2πft + θ) = Asin(wt + θ),**where θ is π/2

**Velocity (v):**v = (dx)/(dt) = 𝓌Acos(𝓌t + θ)

**Acceleration(a):**a = (dv)/(dt) = -𝓌^2(A)(sin(𝓌t+θ))

**Phase difference between displacement-time graphs:**About 25 seconds

0.79 radians

**Circular Motion and SHM:**The projection of an object in circular motion on a diameter follows simple harmonic motion.

**Energy Changes in Simple Harmonic Motion:****Kinetic energy**: KE= ½(m𝓌^2A^2)Total energy remains constant in the absence of dissipative forces.

**Waves and their types:****Mechanical waves:**require a material medium to travel**Electromagnetic waves:**can travel through a vacuum.

**Describing Waves:****Wavefront:**A surface perpendicular to the direction of wave travel.**Amplitude (A):**Maximum displacement from equilibrium.**Wavelength (⅄):**Shortest distance between two points in phase on a wave.**Period (T):**Time for a complete wavelength to pass a fixed point.**Frequency (f):**Number of wavelengths passing through a fixed point per unit time.f = 1/T

__4.2 Traveling waves__

__4.2 Traveling waves__

**Transverse waves:**Direction of vibration perpendicular to the direction of propagation.**Longitudinal waves:**Direction of vibration parallel to the direction of propagation.**Wave Equation:**The velocity of a wave (c) is given by c = f⅄

**Electromagnetic waves:**Travel with varying electric and magnetic fields at 3 x 10^8 m/s in a vacuum.

__4.3 Wave characteristics__

__4.3 Wave characteristics__

**Intensity of Waves:**Intensity (I) is power received per unit area. I = (P)/(4πr^2) and is proportional to the square of amplitude (A^2).

Example:

Intensity at 120m from source: 3 x 10^-6 W/m^2.

**Principle of Superposition:**When two waves meet, the total displacement is the vector sum of their individual displacements.

**Polarization:**Restriction of oscillation direction to a plane perpendicular to the direction of propagation. Result: Plane-polarized light.

**Malus’s Law:**Intensity (I) transmitted by an analyzer is proportional to cos^2(θ) where θ is the angle between the polarizer and the analyzer.

__4.4 Wave Behaviour__

__4.4 Wave Behaviour__

**Laws Of Reflection And Refraction:**Incident, reflected, and refracted rays, and normal lie on the same plane.

The angle of incidence equals the angle of reflection.

*(sinθ1)/(sinθ2) = 1/n*(Snell’s Law)

**Reversibility of Light:***(sinθ1)/(sinθ2) = 1/n_2*for light going from medium 1 to medium 2, and*(sinθ1)/(sinθ2) = 1/n_1*for light traveling in the opposite direction.

**Critical Angle And Total Internal Reflection:**The angle of incidence for which the angle of refraction reaches the right angle is the critical angle.

Total internal reflection occurs when the angle of incidence is greater than the critical angle.

**Double-Slit Interference:**Two coherent sources create interference patterns. Constructive interference occurs at nλ and is destructive at (n + ½)λ.

**Example:**The path difference at point P is 7λ. The nature of the fringe at P is bright, and there are 7 dark fringes between O and P.

**Diffraction:**Wave passed through a narrow gap forms bright and dark fringes. Angular position of minima given by θ = (nλ/a).

**Example:**Path difference at point P is 7λ.

The nature of fringe at P is bright, and there are 7 dark fringes between O and P.

**Interference With Multiple Slits:**More slits result in sharper and more intense maxima and minima.

**Dispersion:**Different wavelengths of light refract at different angles. White light disperses into its constituent wavelengths.

**Resolution:**Rayleigh's criterion states two points are just resolved if the central maximum of the first point falls on the first minimum of the second point.

**Diffraction Grating:**For a grating with N slits, R = λ/change in λ = mN

**Reflection Of Light Off Thin Films:**Reflected light undergoes a phase change of 180∘ if reflected off a denser medium.

A thin film of thickness t, refractive index n, and incident wavelength λ exhibits interference.

**Doppler Effect In Light:**The change in frequency of the light wave is (v/c)(f_0).

**Water Waves:**Follow laws similar to light. Exhibit reflection, refraction, interference, and diffraction.

**Wave Propagation:**Wavefront consists of infinite new disturbance centers.

Successive wavefronts result from wavelets from these disturbances.

**Reflection Of Water Wave:**When a wave hits a barrier, it behaves as if a similar wave is coming from the barrier in the opposite direction.

**Doppler Effect In Sound:**The frequency of a moving source changes for an observer at rest or moving toward/away from the source.

__4.5 Standing waves__

__4.5 Standing waves__

**Boundary Conditions:**Reflected off a fixed boundary suffers a phase change of 180∘.

No change in the phase of a free boundary.

**Standing Waves:**Formed when two waves of equal amplitude and frequency traveling in opposite directions are superimposed.

Positions of crests and troughs do not change with time.

**Nodes and Antinodes:**Nodes are points with zero displacement, antinodes are points with maximum displacement.

**Harmonics On A String:**The string is tied at one end and connected to a vibration generator at the other.

Harmonics formed with increasing loops at

*n*times the frequency of the first harmonic.

**Displacement of string at different times:**Quarter of a cycle: t = 1/4f

Half of a cycle: t = 1/2f

**Frequency of vibration of the spring:**Wavelength 2L, wave velocity 240 m/s, frequency 120 Hz.

**Harmonics In A Pipe:**Harmonics formed with one end open or both ends open. Nodes form at closed ends and antinodes at open ends.

**Explanation regarding refraction of light:**The speed of light is faster in a vacuum than in water, bending away from normal.

**The critical angle for total internal reflection:**sinፀ_c = 1/n

where

*n*is the relative refractive index of denser material with respect to rarer material.

**Frequency of the first harmonic if both ends are open:**Twice the frequency of the first harmonic when one end is closed