IB Physics: C2: Waves Day 2

Wave Reflection at a Boundary

Waves bounce back when they hit a barrier

Direction of Reflected Wave

Opposite to the incident (forward) wave

Superposition Principle

When waves cross, their displacements add together

Resultant Wave

The wave formed by adding the displacements of overlapping waves (e.g., pink + green)

Standing Wave Definition

A wave pattern formed by the superposition of a forward and reflected wave

Conditions for Standing Waves

Forward and reflected waves must have the same wavelength and frequency

Node

A point on a standing wave with zero displacement ("No" movement)

Antinode

A point on a standing wave with maximum amplitude

Node-to-Node Distance

Half a wavelength (λ/2)

Antinode-to-Antinode Distance

Half a wavelength (λ/2)

Node-to-Antinode Distance

Quarter of a wavelength (λ/4)

Harmonics Definition

Specific wavelengths that "fit" on a vibrating medium given its boundary conditions

Boundary Condition: Fixed String

Both ends must be Nodes

Visual: 1st Harmonic (String)

One single loop (football shape)

Wavelength: 1st Harmonic (String)

λ = 2L

Visual: 2nd Harmonic (String)

Two loops (one full sine wave)

Wavelength: 2nd Harmonic (String)

λ = L

Visual: 3rd Harmonic (String)

Three loops

Wavelength: 3rd Harmonic (String)

λ = 2L/3

General Wavelength Formula (String)

λ = 2L/n

Harmonic Series (String)

Includes all integers (n = 1, 2, 3…)

Closed Pipe Instrument

A tube open at one end and closed at the other

Boundary Condition: Closed End

Must be a Node

Boundary Condition: Open End

Must be an Antinode

Allowed Harmonics (Closed Pipe)

Odd integers only (1, 3, 5…)

Why no even harmonics in Closed Pipes?

Even fractions of waves (like 1/2 or 1) do not fit the Node-Antinode boundary condition

Visual: 1st Harmonic (Closed Pipe)

1/4 of a wave loop

Wavelength: 1st Harmonic (Closed Pipe)

λ = 4L

Visual: 2nd Harmonic (Closed Pipe)

Does not exist

Visual: 3rd Harmonic (Closed Pipe)

3/4 of a wave loop (one full loop + half loop)

Wavelength: 3rd Harmonic (Closed Pipe)

λ = 4L/3

General Wavelength Formula (Closed Pipe)

λ = 4L/n (where n is odd)

Open-Open Pipe Instrument

A tube open at both ends

Boundary Condition: Open-Open

Both ends must be Antinodes

Visual: 1st Harmonic (Open Pipe)

Node in the center, Antinodes at edges

Wavelength: 1st Harmonic (Open Pipe)

λ = 2L

Harmonic Series (Open Pipe)

Same frequencies/wavelengths as a string (n = 1, 2, 3…)

General Wavelength Formula (Open Pipe)

λ = 2L/n

Fundamental Wave Property

Frequency is determined by the source and is fundamental

Wavelength Dependence

Wavelength changes based on the medium the wave travels through

Wave Speed Formula

v = λf

Wave Speed Calculation: Frequency

30 Hz (given in example)

Wave Speed Calculation: Length

72 cm (given in example)

Unit Conversion for Calculation

72 cm must be converted to 0.72 meters

Wave Speed Calculation Result

v = 0.72 m * 30 Hz = 21.6 m/s

Relationship: Length vs Wavelength (Fundamental String)

The length of the string is half the wavelength (L = λ/2)