IB PHYSICS Topic 9: Wave phenomena

# 9.1 Introduction to Waves

It transfers energy.

Usually involves a periodic, repetitive movement.

Does not result in a net movement of the medium or particles in the medium (mechanical wave).

There are some basic descriptors of a wave.

**Wavelength**is the distance between two successive identical parts of the wave.**Amplitude**is the maximum displacement from the neutral position.This represents the energy of the wave. Greater amplitude carries greater energy.

**Displacement**is the position of a particular point in the medium as it moves as the wave passes.Maximum displacement is the amplitude of the wave

Frequency (ƒ) is the number of repetitions per second in Hz, and Period (T) is the time for one wavelength to pass a point.

The velocity (v) of the wave is the speed at which a specific part of the wave passes a point. The speed of a light wave is c.

# 9.2 Types of Waves

**Transverse Waves**Waves in which the medium moves at right angles to the direction of the wave.

The high point of a transverse wave is a crest. The low part is a trough.

**Examples of transverse waves:**Water waves (ripples of gravity waves, not sound through water)

Light waves

S-wave earthquake waves

Stringed instruments

Torsion wave

**Longitudinal Waves:**A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.

**Parts of longitudinal waves**:**Compression:**where the particles are close together.**Rarefaction:**where the particles are spread apart.

**Examples of longitudinal waves:**Sound waves

P-type earthquake waves

Compression wave

**Mechanical waves:**

A wave which needs a medium to propagate itself.

Sound waves, waves in a slinky, and water waves are all examples of this.

**Matter Waves:**

Any moving object can be described as a wave.

When a stone is dropped into a pond, the water is disturbed from its equilibrium position as the wave passes; it returns to its equilibrium position after the wave has passed.

**Electromagnetic Waves:**

These waves are disturbance that does not need any object medium for propagation and can easily travel through the vacuum.

They are produced due to various magnetic and electric fields.

The periodic changes that take place in magnetic and electric fields and therefore known as electromagnetic waves.

# 9.3 Properties of Waves

The prime properties of waves are as follows:

**Amplitude –**Wave is an energy transport phenomenon.Amplitude is the height of the wave, usually measured in metres.

It is directly related to the amount of energy carried by a wave.

**Wavelength –**The distance between identical points in the adjacent cycles of crests of a wave is called a wavelength.It is also measured in metres.

**Period –**The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.As the period is time, hence is measured in units of time such as seconds or minutes.

**Frequency –**The frequency of a wave is the number of waves passing a point in a certain time.The unit of frequency is hertz (Hz) which is equal to one wave per second.

The period is the reciprocal of the frequency and vice versa.

**Speed –**The speed of an object means how fast an object moves and is usually expressed as the distance travelled per time of travel.The speed of a wave refers to the distance travelled by a given point on the wave (crest) in a given interval of time.

The speed of a wave is thus measured in metres/second i.e. m/s.

# 9.4 Simple Harmonic Motion

**Definition:****Simple Harmonic Motion (SHM)**is described by Newton's Second Law through the following equations:**x = x_0(cos(ωt))****v = -ωx_0(sin(ωt))****a = -ω^2(x_0)(cos(ωt))**

Here,

**x_0 is the amplitude (maximum displacement),****x is the displacement,****v is the velocity, a is the acceleration, and****ω is the angular frequency related to the period (T) through ω= 2π/T.**

**Energy Changes:**In SHM, there's an exchange between kinetic energy (KE) and potential energy (PE) throughout the motion, while the total energy (KE + PE) remains constant.

# 9.5 Difference between Periodic, Oscillation and Simple Harmonic Motion

**Periodic Motion**A motion repeats itself after an equal interval of time. For example, uniform circular motion.

There is no equilibrium position.

There is no restoring force.

There is no stable equilibrium position.

**Oscillation Motion**To and fro motion of a particle about a mean position is called an oscillatory motion in which a particle moves on either side of the equilibrium (or) mean position is an oscillatory motion.

It is a kind of periodic motion bounded between two extreme points.

For example

**, the oscillation of a simple pendulum, spring-mass system.**The object will keep on moving between two extreme points about a fixed point is called the mean position (or) equilibrium position along any path (the path is not a constraint).

A restoring force will be directed towards the equilibrium position (or) mean position.

**In an oscillatory motion,**the net force on the particle is zero at the mean position.The mean position is a stable equilibrium position.

**Simple Harmonic Motion or SHM**It is a special case of oscillation, along with a straight line between the two extreme points (the path of SHM is a constraint).

The path of the object needs to be a straight line.

A restoring force will be directed towards the equilibrium position (or) mean position.

**The mean position in Simple Harmonic Motion is a stable equilibrium.**

**Summary:**

At maximum displacement, PE is at its maximum while KE is zero.

At zero displacement, KE is at its maximum while PE is zero.

At minimum displacement, PE is at its maximum while KE is zero.

Total energy remains constant throughout the motion.

# 9.6 Single-Slit Diffraction

**Nature of Single-Slit Diffraction:**Distinct diffraction patterns emerge when light passes through a single slit comparable in size to the wavelength of the light.

**Representation of Diffraction Pattern:**This pattern is represented by plotting light intensity against the angle of diffraction.

**Angle of Diffraction for First Minimum θ:**sinθ =

*λ*/aHere, λ is the wavelength, and a is the size/length of the slit.

sinθ_

*m*=*m*(*λ*/D)Where

*m*is the order of the maximum, D is the distance from the slit to the screen.

# 9.7 Interference

**Young’s Double-Slit Experiment:**In this experiment, interference patterns are observed when light passes through two slits, creating regions of constructive and destructive interference.

**Modulation of Double-Slit Pattern by Single-Slit Diffraction:**A true double-slit pattern shows closely spaced dark and light areas, superimposed over the single-slit pattern.

The single-slit profile modulates the double-slit pattern.

**Multiple Slit and Diffraction Grating Interference Patterns:****Multiple Slit Interference Patterns:**θ = m(λ/a)

**Diffraction Grating Interference Patterns:***d*sinθ = mλWhere

*d*is the distance between gratings, m is the order of the maximum, and λ is the wavelength.

# 9.8 Resolution

**Diffracting Aperture Size:**The resolution of an image passing through a diffracting aperture improves with a larger aperture diameter.

**Resolution of Two-Source Systems:**The Rayleigh criterion determines whether two points are just resolved. The minimum angular separation θ for two points to be just resolved is given by θ = 1.22(λ/a)

**Importance of Resolution in Technology:**Resolution is crucial in technologies like CDs, DVDs, electron microscopes, and radio telescopes for optimal performance.

# 9.9 Doppler Effect

**Doppler Effect Equations for Sound Waves:**Four Doppler effect equations cater to different cases based on the movement of the source and/or observer.

**Doppler Equation for Electromagnetic Waves:**change in f = (v/c)f

This equation is applicable when the velocity of the observer is much smaller than the speed of light.

**Application in Speed Detectors:**The Doppler effect is utilized in speed detectors where the frequency shift indicates whether a car is approaching or moving away, enabling the calculation of the car's speed.

# IB PHYSICS Topic 9: Wave phenomena

# 9.1 Introduction to Waves

It transfers energy.

Usually involves a periodic, repetitive movement.

Does not result in a net movement of the medium or particles in the medium (mechanical wave).

There are some basic descriptors of a wave.

**Wavelength**is the distance between two successive identical parts of the wave.**Amplitude**is the maximum displacement from the neutral position.This represents the energy of the wave. Greater amplitude carries greater energy.

**Displacement**is the position of a particular point in the medium as it moves as the wave passes.Maximum displacement is the amplitude of the wave

Frequency (ƒ) is the number of repetitions per second in Hz, and Period (T) is the time for one wavelength to pass a point.

The velocity (v) of the wave is the speed at which a specific part of the wave passes a point. The speed of a light wave is c.

# 9.2 Types of Waves

**Transverse Waves**Waves in which the medium moves at right angles to the direction of the wave.

The high point of a transverse wave is a crest. The low part is a trough.

**Examples of transverse waves:**Water waves (ripples of gravity waves, not sound through water)

Light waves

S-wave earthquake waves

Stringed instruments

Torsion wave

**Longitudinal Waves:**A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.

**Parts of longitudinal waves**:**Compression:**where the particles are close together.**Rarefaction:**where the particles are spread apart.

**Examples of longitudinal waves:**Sound waves

P-type earthquake waves

Compression wave

**Mechanical waves:**

A wave which needs a medium to propagate itself.

Sound waves, waves in a slinky, and water waves are all examples of this.

**Matter Waves:**

Any moving object can be described as a wave.

When a stone is dropped into a pond, the water is disturbed from its equilibrium position as the wave passes; it returns to its equilibrium position after the wave has passed.

**Electromagnetic Waves:**

These waves are disturbance that does not need any object medium for propagation and can easily travel through the vacuum.

They are produced due to various magnetic and electric fields.

The periodic changes that take place in magnetic and electric fields and therefore known as electromagnetic waves.

# 9.3 Properties of Waves

The prime properties of waves are as follows:

**Amplitude –**Wave is an energy transport phenomenon.Amplitude is the height of the wave, usually measured in metres.

It is directly related to the amount of energy carried by a wave.

**Wavelength –**The distance between identical points in the adjacent cycles of crests of a wave is called a wavelength.It is also measured in metres.

**Period –**The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.As the period is time, hence is measured in units of time such as seconds or minutes.

**Frequency –**The frequency of a wave is the number of waves passing a point in a certain time.The unit of frequency is hertz (Hz) which is equal to one wave per second.

The period is the reciprocal of the frequency and vice versa.

**Speed –**The speed of an object means how fast an object moves and is usually expressed as the distance travelled per time of travel.The speed of a wave refers to the distance travelled by a given point on the wave (crest) in a given interval of time.

The speed of a wave is thus measured in metres/second i.e. m/s.

# 9.4 Simple Harmonic Motion

**Definition:****Simple Harmonic Motion (SHM)**is described by Newton's Second Law through the following equations:**x = x_0(cos(ωt))****v = -ωx_0(sin(ωt))****a = -ω^2(x_0)(cos(ωt))**

Here,

**x_0 is the amplitude (maximum displacement),****x is the displacement,****v is the velocity, a is the acceleration, and****ω is the angular frequency related to the period (T) through ω= 2π/T.**

**Energy Changes:**In SHM, there's an exchange between kinetic energy (KE) and potential energy (PE) throughout the motion, while the total energy (KE + PE) remains constant.

# 9.5 Difference between Periodic, Oscillation and Simple Harmonic Motion

**Periodic Motion**A motion repeats itself after an equal interval of time. For example, uniform circular motion.

There is no equilibrium position.

There is no restoring force.

There is no stable equilibrium position.

**Oscillation Motion**To and fro motion of a particle about a mean position is called an oscillatory motion in which a particle moves on either side of the equilibrium (or) mean position is an oscillatory motion.

It is a kind of periodic motion bounded between two extreme points.

For example

**, the oscillation of a simple pendulum, spring-mass system.**The object will keep on moving between two extreme points about a fixed point is called the mean position (or) equilibrium position along any path (the path is not a constraint).

A restoring force will be directed towards the equilibrium position (or) mean position.

**In an oscillatory motion,**the net force on the particle is zero at the mean position.The mean position is a stable equilibrium position.

**Simple Harmonic Motion or SHM**It is a special case of oscillation, along with a straight line between the two extreme points (the path of SHM is a constraint).

The path of the object needs to be a straight line.

A restoring force will be directed towards the equilibrium position (or) mean position.

**The mean position in Simple Harmonic Motion is a stable equilibrium.**

**Summary:**

At maximum displacement, PE is at its maximum while KE is zero.

At zero displacement, KE is at its maximum while PE is zero.

At minimum displacement, PE is at its maximum while KE is zero.

Total energy remains constant throughout the motion.

# 9.6 Single-Slit Diffraction

**Nature of Single-Slit Diffraction:**Distinct diffraction patterns emerge when light passes through a single slit comparable in size to the wavelength of the light.

**Representation of Diffraction Pattern:**This pattern is represented by plotting light intensity against the angle of diffraction.

**Angle of Diffraction for First Minimum θ:**sinθ =

*λ*/aHere, λ is the wavelength, and a is the size/length of the slit.

sinθ_

*m*=*m*(*λ*/D)Where

*m*is the order of the maximum, D is the distance from the slit to the screen.

# 9.7 Interference

**Young’s Double-Slit Experiment:**In this experiment, interference patterns are observed when light passes through two slits, creating regions of constructive and destructive interference.

**Modulation of Double-Slit Pattern by Single-Slit Diffraction:**A true double-slit pattern shows closely spaced dark and light areas, superimposed over the single-slit pattern.

The single-slit profile modulates the double-slit pattern.

**Multiple Slit and Diffraction Grating Interference Patterns:****Multiple Slit Interference Patterns:**θ = m(λ/a)

**Diffraction Grating Interference Patterns:***d*sinθ = mλWhere

*d*is the distance between gratings, m is the order of the maximum, and λ is the wavelength.

# 9.8 Resolution

**Diffracting Aperture Size:**The resolution of an image passing through a diffracting aperture improves with a larger aperture diameter.

**Resolution of Two-Source Systems:**The Rayleigh criterion determines whether two points are just resolved. The minimum angular separation θ for two points to be just resolved is given by θ = 1.22(λ/a)

**Importance of Resolution in Technology:**Resolution is crucial in technologies like CDs, DVDs, electron microscopes, and radio telescopes for optimal performance.

# 9.9 Doppler Effect

**Doppler Effect Equations for Sound Waves:**Four Doppler effect equations cater to different cases based on the movement of the source and/or observer.

**Doppler Equation for Electromagnetic Waves:**change in f = (v/c)f

This equation is applicable when the velocity of the observer is much smaller than the speed of light.

**Application in Speed Detectors:**The Doppler effect is utilized in speed detectors where the frequency shift indicates whether a car is approaching or moving away, enabling the calculation of the car's speed.