Oscillations and Waves

Wave Characteristics

Progressive Waves

Any wave that moves through or across a medium (e.g. water or even a vacuum) carrying energy away from its source is a progressive (travelling) wave.

E.g. A duck on water:

As the wave passes the duck, the water (and duck) only oscillate vertically.

Wave direction Duc

k os

cilla

tion

This illustrates that there is no net transfer of the medium through which the wave travels, only energy moves from place to place.

In many examples, the wave carrying medium will oscillate with simple harmonic motion (i.e. a -x).

Types of Wave

Waves can be described as transverse or longitudinal.

In a transverse wave the vibration (oscillation) of particles is at right angles to the direction of energy transfer. Transverse waves cannot move through a gas. Examples:

In a longitudinal wave the vibration of particles is in the same plane as the direction of energy transfer.Examples:

Oscillation Energy transfer

Transverse:

Longitudinal:

Energy Transfer

(Label a crest (peak), trough, rarefaction, compression)

Describing Waves

Crest and trough: Points on the wave where particles are oscillating at maximum positive and negative displacement.

Rarefaction and compression: Areas in a longitudinal wave where particles are far apart (lower than normal density) and close together (higher than normal density).

Wave graphs

Waves can be represented graphically in two ways:

1. Displacement - Distance:

2. Displacement – Time:

Wavelength

Amplitude

Distance

Dis

pla

cem

ent

Time Period

Amplitude

Time

Dis

pla

cem

ent

The following terms and descriptions are mixed up:

Intensity of a wave is the ‘power per unit area’ incident upon a surface, in Wm-2. (It is proportional to the square of the amplitude, so I A2)

Term Description

1. Wavelength (λ) a. The maximum displacement from the equilibrium position (in metres, m)

2. Amplitude (A) b. The distance moved by a wave crest per second (in metres per second, ms-1)

3. Frequency (f) c. The time required for the wave to complete one oscillation (in seconds, s)

4. Periodic Time (T) d. The distance between two successive crests (in metres, m)

5. Speed (v) e. The number of waves completed in one second (in Hertz, Hz)

Term Description

1. Wavelength (λ) d. The distance between two successive crests (in metres, m)

2. Amplitude (A)

3. Frequency (f)

4. Periodic Time (T)

5. Speed (v)

Term Description

1. Wavelength (λ) d. The distance between two successive crests (in metres, m)

2. Amplitude (A) a. The maximum displacement from the equilibrium position (in metres, m)

3. Frequency (f)

4. Periodic Time (T)

5. Speed (v)

Term Description

1. Wavelength (λ) d. The distance between two successive crests (in metres, m)

2. Amplitude (A) a. The maximum displacement from the equilibrium position (in metres, m)

3. Frequency (f) e. The number of waves completed in one second (in Hertz, Hz)

4. Periodic Time (T)

5. Speed (v)

Term Description

1. Wavelength (λ) d. The distance between two successive crests (in metres, m)

2. Amplitude (A) a. The maximum displacement from the equilibrium position (in metres, m)

3. Frequency (f) e. The number of waves completed in one second (in Hertz, Hz)

4. Periodic Time (T) c. The time required for the wave to complete one oscillation (in seconds, s)

5. Speed (v)

Term Description

1. Wavelength (λ) d. The distance between two successive crests (in metres, m)

2. Amplitude (A) a. The maximum displacement from the equilibrium position (in metres, m)

3. Frequency (f) e. The number of waves completed in one second (in Hertz, Hz)

4. Periodic Time (T) c. The time required for the wave to complete one oscillation (in seconds, s)

5. Speed (v) b. The distance moved by a wave crest per second (in metres per second, ms-1)

The Wave Equation

In a time of one full period (t = T), a point in a wave will move forward through one a distance of one whole wavelength (d = λ).

so…

substituting gives…

This is called the ‘wave equation’

Speed = Distance Time

Wave speed = Wavelength Time period

v = λ T

but… T = 1 f

v = f λ

Electromagnetic Waves

The visible spectrum of light (Roy G Biv) is just a small part of a larger group of electromagnetic waves known as the ‘electromagnetic spectrum’.

All electromagnetic radiation:

• exists as variations in electrical and magnetic fields

• travels at 3 x 108 ms-1 (300 000 000 ms-1)• can travel through a vacuum• carries energy • has wave behaviour (obeying v = fλ)