# Physics, Waves and WPD, 5-8

## Waves

### Progressive Waves

Progressive waves transfer energy without transferring any matter. There is no net movement of the medium, although each particle does oscillate around its equilibrium position.

#### Transverse Waves

In a transverse wave, particles oscillate at right angles to the direction of propagation.

#### Longitudinal Waves

In a longitudinal wave, particles oscillate parallel to the direction of propagation. These have compressions and rarefactions.

#### Mechanical and Electromagnetic Waves

Mechanical waves transfer energy through a medium by the oscillation of particles, and can be transverse or longitudinal.

EM waves are not mechanical, and no not require a medium to propagate.

• Linked electric and magnetic fields

• Regions of space when an electric charge would experience a force

• As an EM wave passes, the electric and magnetic fields oscillate

• Electric field changes, inducing a magnetic filed perpendicularly

• Magnetic field varies, changing electric field

• Wave is self perpetuating

• EM waves are always transverse

### Wave Properties

• Displacement is measured from the equilibrium position, and can be positive or negative

• Maximum displacement is equal to the amplitude

• The amount of energy transferred by a wave is dependent on its amplitude

• Wavelength sis the distance between two consecutive points with identical displacement and velocity

#### Phase

• Two points exactly one wavelength apart are in phase - they oscillate in step with each other

• Two points half a wavelength apart are in antiphase

• Phase difference is dependent on the fraction of a wavelength between two points

• One wavelength is represented by 360°

• Two points with a phase difference of 360°are in phase

• Two points with a phase difference of 180°are in antiphase

• One radian is equivalent to 180°

• $$360^{\circ}=2\pi$$

#### Frequency

The time taken for one complete wave to pass a certain point is its period, $$T$$. The phase difference can then be described as the fraction of a period between two points.

\begin{gather*} f=\frac{1}{T} \\ T=\frac{1}{f} \\ \end{gather*}

### Wave Speed

The speed of a wave depends on the properties of the medium. For a mechanical wave, it depends on:

• The size of the forces between oscillating particles - the elasticity of the medium

• The intertia of the vibrating particles - how easy or difficult it is to accelerate each particle

• Sound travels faster through solids because of the stronger forces between adjacent particles

• $$v=f\lambda$$