Wave behaviors

Physics Notes — Waves

Based on the uploaded lesson notes.

Waves in One Dimension

Mechanical vs Electromagnetic Waves

Mechanical Waves

• Require a medium to travel.

• Examples:

  • sound waves

  • water waves

  • spring waves

Electromagnetic Waves

• Do not require a medium.

• Can travel through a vacuum.

• Examples:

  • light

  • microwaves

  • radio waves

Wave Reflection

Reflection

When a wave hits a boundary and bounces back.

Important Facts

• Reflected wave travels in opposite direction.

• Speed stays the same if medium stays the same.

• Wavelength also stays the same.

• Amplitude may change.

• Some reflected waves invert (flip upside down).

Examples

• mirror reflections

• echoes

• water waves hitting a wall

Superposition and Interference

Superposition Principle

When two waves meet, the resultant displacement equals the sum of the individual displacements.

R=A+BR=A+BR=A+B

Constructive Interference

Occurs when waves are in phase.

In Phase

• crests align with crests

• troughs align with troughs

Result

• amplitudes add

• bigger wave forms

Example:

100+50=150100+50=150100+50=150

Destructive Interference

Occurs when waves are out of phase.

Out of Phase

• crest overlaps trough

Result

• amplitudes subtract

• smaller wave forms

Example:

75+(−50)=2575+(-50)=2575+(−50)=25

If equal amplitudes meet out of phase:

A+(−A)=0A+(-A)=0A+(−A)=0

Complete cancellation occurs.

Transmission

Transmission

When part of a wave enters a new medium.

Key Ideas

• Some energy reflects.

• Some energy transmits.

• Wave speed changes in the new medium.

• Wavelength changes.

• Frequency stays constant.

Faster → Slower Medium

• speed decreases

• wavelength decreases

Waves in Two Dimensions

Point Source Waves

Waves spreading outward from one point form concentric circles.

Examples:

• water ripples

• sound from speakers

• light from bulbs

Reflection in Two Dimensions

Waves reflect from boundaries similarly to 1D waves.

Law of Reflection

The angle of incidence equals the angle of reflection.

θi=θr\theta_i=\theta_rθi​=θr​

Definitions

• angle of incidence = incoming angle

• angle of reflection = reflected angle

• normal = perpendicular line to the surface

Refraction

Refraction

Bending of waves when entering a new medium.

Why?

Wave speed changes.

Effects

• direction changes

• wavelength changes

• frequency remains constant

Example

• straw appearing bent in water

Huygens’s Principle

Developed by Christiaan Huygens.

Principle

Every point on a wave front acts as a source of secondary waves.

This explains:

• reflection

• refraction

• diffraction

Diffraction

Diffraction

Bending of waves around obstacles or through openings.

Occurs in:

• sound waves

• water waves

• light waves

Examples

• hearing someone behind a wall

• ocean waves around rocks

• light spreading through slits

Important Wave Equations

Wave Speed Equation

v=fλv=f\lambdav=fλ

fff

Hz

λ\lambdaλ

m

f es la frecuencia; λ es la longitud de onda; v es la velocidad de onda.

v=fλ=2×3=6 m/sv=f\lambda=2\times 3=6\,\text{m/s}v=fλ=2×3=6m/s

λ

Where:

• vvv = wave speed

• fff = frequency

• λ\lambdaλ = wavelength

Frequency and Period

Frequency

Number of oscillations per second.

Measured in hertz (Hz).

Period

Time for one complete cycle.

Relationship:

T=1fT=\frac{1}{f}T=f1​

TTT

s

T es el período; f es la frecuencia.

f=1T=12=0.5 Hzf=\frac{1}{T}=\frac{1}{2}=0.5\,\text{Hz}f=T1​=21​=0.5Hz

Tf = 0.5 Hz

and

f=1Tf=\frac{1}{T}f=T1​

TTT

s

T es el período; f es la frecuencia.

f=1T=12=0.5 Hzf=\frac{1}{T}=\frac{1}{2}=0.5\,\text{Hz}f=T1​=21​=0.5Hz

Tf = 0.5 Hz

Amplitude

Amplitude

Maximum displacement from equilibrium.

• larger amplitude = more energy

Wave Vocabulary