Properties of Waves

Travelling waves are defined as follows:

Oscillations that transfer energy from one place to another without transferring matter

Waves transfer energy, not matter
Waves are generated by oscillating sources
- These oscillations travel away from the source

Oscillations can propagate through a medium (e.g. air, water) or in vacuum (i.e. no particles), depending on the type of wave

The key properties of travelling waves are as follows:

Displacement

Displacement $x$ of a wave is the distance of a point on the wave from its equilibrium position
- It is a vector quantity; it can be positive or negative
- Measured in metres (m)

Wavelength

Wavelength λ is the length of one complete oscillation measured from the same point on two consecutive waves
- For example, two crests, or two troughs
- Measured in metres (m)

Amplitude

Amplitude A is the maximum displacement of an oscillating wave from its equilibrium position (x = 0)
- Amplitude can be positive or negative depending on the direction of the displacement
- Measured in metres (m)
- Where the wave has 0 amplitude (the horizontal line) is referred to as the equilibrium position

Amplitude and wavelength

Diagram showing the amplitude and wavelength of a wave

Period & Frequency

Period (T) is the time taken for a complete oscillation to pass a fixed point
- Measured in seconds (s)

Frequency (f) is the number of complete oscillations to pass a fixed point per second
- Measured in Hertz (Hz)

The frequency, f, and the period, T, of a travelling wave are related to each other by the equation:

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

Where:
- f = frequency (Hz)
- T = time period (s)

4-2-1-period-and-frequency_sl-physics-rn

Period T and frequency f of a travelling wave

Wave speed

Wave speed (v) is the distance travelled by the wave per unit time
- Measured in metres per second (m s^-1)

The wave speed is defined by the equation:

$v = f λ = \frac{λ}{T}$

Where:
- v = wave speed (m s^–1)
- λ = wavelength (m)

This is referred to as the wave equation
It tells us that for a wave of constant speed:
- As the wavelength increases, the frequency decreases
- As the wavelength decreases, the frequency increases

Frequency and wavelength, downloadable AS & A Level Physics revision notes

The relationship between the frequency and wavelength of a wave

Worked example

The graph below shows a travelling wave.

4-2-1-we-properties-of-wave-question-graph Determine:

(a) The amplitude A of the wave, in m.

(b) The frequency f of the wave, in Hz.

Answer:

(a) Identify the amplitude A of the wave on the graph

The amplitude is defined as the maximum displacement from the equilibrium position (x = 0)

The amplitude must be converted from centimetres (cm) into metres (m)

A = 0.1 m

(b) Calculate the frequency of the wave

Step 1: Identify the period T of the wave on the graph

The period is defined as the time taken for one complete oscillation to occur

4-2-1-we-properties-of-wave-step-2

The period must be converted from milliseconds (ms) into seconds (s)

T = 1 × 10^–3 s

Step 2: Write down the relationship between the frequency f and the period T

f = \frac{1}{T}

Step 3: Substitute the value of the period determined in Step 1

$f = \frac{1}{1 \times 10^{- 3}} = 1000 Hz$

Worked example

The wave in the diagram below has a speed of 340 m s^–1. WE - Wave equation question image, downloadable AS & A Level Physics revision notes

Determine the wavelength of the wave.

Answer:

Worked example

A travelling wave has a period of 1.0 μs and travels at a velocity of 100 cm s^–1.

Calculate the wavelength of the wave, in m.

Answer:

Step 1: Write down the known quantities

Period, T = 1.0 μs = 1.0 × 10^–6 s
Velocity, v = 100 cm s^–1 = 1.0 m s^–1

Note the conversions:

- The period must be converted from microseconds (μs) into seconds (s)
- The velocity must be converted from cm s^–1 into m s^–1

Step 2: Write down the relationship between the frequency f and the period T

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

Step 3: Substitute the value of the period into the above equation to calculate the frequency

$f = \frac{1}{1 \times 10^{- 6}} = 1 \times 10^{6}$

Step 4: Write down the wave equation

$v = f λ$

Step 5: Rearrange the wave equation to calculate the wavelength λ

$λ = \frac{f}{v}$

Step 6: Substitute the numbers into the above equation

$λ = \frac{1}{1 \times 10^{6}} = 1 \times 10^{- 6}$

Examiner Tip

You must be able to interpret different properties of waves from a variety of graphs. You may recognise calculating the time period and wavelength look very similar (the distance for one full wave). This is the time period if the x-axis is time. If the x-axis is distance, then this distance is the wavelength.

Pay very close attention to units. If you want a frequency in Hertz, then the time period must be in seconds and not milliseconds etc.

Properties of Waves (SL IB Physics)

Revision Note