Determining Wave SpeedUniversal Wave Equation

Example – calculate wave speedA harp string supports a wave

with a wavelength of 2.3m and a frequency of 220.0 Hz. Calculate its wave speed

Example – calculate wavelengthA trumpet produces a sound wave

that is observed travelling at 350 m/s with a frequency of 1046.50 Hz. Calculate the wavelength of the sound wave.

Factors that affect wave speedTemperature

Linear Density

Reflection What will happen to the wave pulses shown

below?

Link to video (blip.tv)

A: Wave pulse heading towards a wall.

B: Wave pulse heading towards a “free end”.

Reflection & Transmission

When a wave moves from one medium to another, its speed changes but its frequency remains the same.

What else happens when waves move from one medium to another? What will happen to the pulses shown below?

A: Wave pulse travelling from a thinner rope into a thicker rope.

(Less Dense More Medium, Faster Slower)

B: Wave pulse travelling from a thicker rope into a thinner rope.

(More Dense Less Dense, Slower Faster)

Interference of Waves Principle of Superposition:

The resultant displacement is the sum of the displacements of each component wave.

Interference of Waves

What happens after the waves interfere with each other?

Interference of WavesWhat happens when the wave pulses

shown below meet?P

position / m

1m

t = 0 s

P

t = 1 s

P

t = 2 s

P

t = 3 s

position / m

position / m

position / m

Principle of Superposition:The resultant displacement is the sum of the displacements of each component wave.

Interference of WavesP

position / m

1m

t = 0 s

P

t = 1 s

P

t = 2 s

P

t = 3 s

position / m

position / m

position / m

P

position / m

1m

t = 0 s

P

t = 1 s

P

t = 2 s

P

t = 3 s

position / m

position / m

position / m

Interference of Waves Destructive

interference:Resultant displacement is smaller than individual pulses.

Constructive interference:Resultant displacement is greater than individual pulses.

Interference of Waves

Standing Waves When identical periodic waves travel in

opposite directions, they produce a pattern that appears to be standing still. Such waves are known as standing waves.

Parts of a standing wave Nodes

Points on wave that never move

Located half wavelength apart

Antinodes Points that vibrate

maximally

Standing Waves The standing waves can be produced using one

source:a 2nd identical wave is produced by reflection.

For every medium of fixed length, there are many natural frequencies that produce resonance:

Standing Waves Fundamental frequency

Lowest natural frequency, longest wavelength Also called fundamental mode

Overtones Refer to all natural frequencies higher than the fundamental 1st overtone = 1 node, etc.

Harmonics Refer to fundamental & any

overtone Fundamental = 1st harmonic,

1st overtone = 2nd harmonic, etc.

Harmonics

Practice

P. 391 # 1-6

Recap: Properties of WavesReflectionTransmissionRequire a medium in which to travel Interference (Principle of

Superposition) Exhibit constructive & destructive

interference

What are some other properties of waves?

Law of ReflectionThe angle of incidence is

equal to the angle of reflection:

A water wave incident on a barrier.

The dotted line is called the “normal”. The normal line by definition is perpendicular to the barrier.

All angles are measured from the normal.

RefractionWhen waves travel from one

medium into another, their speed changes.

This causes the wave to bend:When water waves travel from deep to shallow water, the speed of the wave decreases.

Since the frequency of waves is constant, because the wave’s speed decreases, its wavelength decreases. (Why?)

Waves travelling from a faster to a slower medium always bend towards the normal.

Diffraction When waves travel past the edges of a barrier

or through a small opening, waves bend & spread:

The amount of diffraction is greatest when the size of the opening is the approx. equal to the wavelength.

2D Interference

2D Interference