# Properties of waves

Waves are one of the ways in which energy may be transferred between stores. Waves can be described as , or about a rest position. For example:

• sound waves cause air particles to vibrate back and forth
• ripples cause water particles to vibrate up and down

The direction of these oscillations is the difference between longitudinal or transverse waves. In , the vibrations are parallel to the direction of wave travel. In , the vibrations are at right angles to the direction of wave travel.

Mechanical waves travel through . They cause oscillations of particles in a solid, liquid or gas. The material through which they travel is called a . Electromagnetic waves cause oscillations in electrical and magnetic fields. They do not need matter to travel through.

All waves transfer energy but they do not transfer matter.

## Parts of a wave

Waves are described using the following terms:

• Rest position - the undisturbed position of particles or fields when they are not vibrating.
• Displacement - the distance that a certain point in the medium has moved from its rest position.
• Peak - the highest point above the rest position.
• Trough - the lowest point below the rest position.
• Amplitude - the maximum displacement of a point of a wave from its rest position.
• Wavelength - distance covered by a full cycle of the wave. Usually measured from peak to peak, or trough to trough.
• Time period - the time taken for a full cycle of the wave. Usually measured from peak to peak, or trough to trough.
• Frequency - the number of waves passing a point each second.

## Wave period and wave speed

The time period of a wave can be calculated using the equation:

$\text{Time period} = \frac{1}{\text{frequency}}$

$\text{T} = \frac{1}{\text{f}}$

This is when:

• time period (T) is measured in seconds (s)
• frequency (f) is measured in hertz (Hz)

### Example calculation

Calculate the time period of a wave with a frequency of 50 Hz.

$\text{T} = \frac{1}{\text{f}}$

$\text{T} = \frac{1}{50}$

$$\text{T}$$ = 0.02 s

Question

Calculate the time period of a wave with a frequency of 400 Hz.

$\text{T} = \frac{1}{400}$

$$\text{T}$$ = 0.0025 s

## Calculating wave speed

The speed of a wave is how fast the wave moves through the medium.

The speed of a wave can be calculated using the equation:

wave speed = frequency × wavelength

$\text{v} = \text{f \lambda}$

This is when:

• wave speed (v) is measured in metres per second (m/s)
• frequency (f) is measured in hertz (Hz)
• wavelength (λ) is measured in metres (m)

### Example calculation

What is the speed of a wave that has a frequency of 50 Hz and a wavelength of 6 m?

$\text{v} = \text{f \lambda}$

$$\text{v}$$ = 50 × 6

$$\text{v}$$ = 300 m/s

Question

What is the speed of a wave with a frequency of 0.2 Hz and a wavelength of 25 m?

$\text{v} = \text{f \lambda }$

$$\text{v}$$ = 0.2 × 25

$$\text{v}$$ = 5 m/s