WAVESSHMTypes of WavesElectromagneticMechanical

TransverseLongitudinalSurface

Wave CharacteristicsReflectionInterferenceStanding Wave

Simple Harmonic Motion

Motion caused by a restoring force that is proportional to displacement

EXAMPLE: Hooks Law

• 𝐹 = −𝑘𝑥

• 𝑘 = 𝑠𝑝𝑟𝑖𝑛𝑔 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑁

𝑚

• 𝑥 = 𝑑𝑖𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑓𝑟𝑜𝑚 𝑟𝑒𝑠𝑡 𝑝𝑜𝑠𝑡𝑖𝑡𝑖𝑜𝑛

• Force is in the opposite direction from displacement

Simple Harmonic Motion• Period = 𝑻= Time for one oscillation

• Frequency =𝒇= oscillations per second (Hertz)

• 𝑇 =1

𝑓𝑓 =

1

𝑇

• 𝒙 = displacement from rest position

• Amplitude= 𝑨 = maximum displacement from rest position

• Period of Oscillating Mass → 𝑻 = 𝟐𝝅𝒎

𝒌

The Simple Pendulum

•𝑇 = 2𝜋𝐿

𝑔

Electromagnetic wave

Requires No Medium to Travel

Oscillating Electric and Magnetic Field

Travel at the speed of light𝑣 = 𝑐 = 3 ∗ 108𝑚/𝑠

Waves: Transfer Energy

Mechanical Wave

• Requires Medium to travel

• Vibrating Matter

Examples:

• Sound

• Ocean Waves

• Earthquakes

3 Types

Transverse

Longitudinal

Surface

Transverse wavesMedium moves perpendicular to the direction of a wave.

Examples:• Slinky• Crowd Waves at Supercross• Bustin’ a Move

Longitudinal WavesMedium moves parallel to the direction of a wave.

Examples:• Sound Wave• Compressed Slinky• Mosh Pit

Surface WaveMedium moves both parallel and perpendicular to the direction of a wave.

Examples:• Wave Pool• Ocean• Great Lakes

Wave characteristics:

Amplitude, A

•Maximum Displacement from rest position

•Determined by energy

• Wavelength, λ

•Distance between corresponding parts of wave.

• Frequency, f

•Determined by the source

•Oscillations per Unit Time

•Measured in Hertz

•Period, T

• Time for one Oscillations

𝑇 =1

𝑓𝑓 =

1

𝑇

Wave characteristics:

VELOCITY

• Speed of a wave is determined by the medium

• 𝑣 = 𝑓𝜆 (m/s)

Single Medium

SAMPLE PROBLEMA satellite Radio Station has a frequency of 137 MHz.

• Determine the period of the wave?

• Determine the wavelength?

An AM radio wave has a wavelength of 395m

• Determine the frequency of the wave?

• What radio station is it?

Reflection• Occurs when a wave bounces off a barrier

Reflection off Rigid Barrier

Reflected wave has opposite Phase

Reflection off Less-Rigid Barrier

Reflected wave has same phase

Reflection

Any time a wave reaches a barrier part of wave reflected, part of wave transmitted

Ratio of reflected to transmitted depends on properties of the two mediums

Destructive Interference• Amplitude decreases• Pulses meet out of phase

Interference

Constructive Interference• Amplitude increases• Pulses meet In-phase

Constructive & DestructiveInterference

• Occurs when two or more waves meet at the same point in a medium at the same time• Causes amplitude to increase or decrease

Interference

Destructive Interference• Amplitude decreases

Principle of Super Position• the displacement of resulting pulse =

sum of the individual displacements

InterferenceConstructive Interference• Amplitude increases

Principle of Super Position• the displacement of resulting pulse id

sum of the individual displacements

Standing wave

• Standing wave has stationary nodes & antinode

ANTINODEProduced by Constructive Interference• Point of maximum displacement• Pulses meet In-phase

NODEProduced by Destructive Interference• Point of no displacement• Pulses meet out of phase

Resonance

Sound wave and glass oscillate at same frequency.

Produces constructive interference

Amplitude of glass vibrations increases until glass breaks

Resonance

Low frequency produced by wind in the river vibrates at the same frequency as the bridge.

Produces standing wave on Bridge