Properties of Waves
- Travelling waves are defined as follows:
Oscillations that transfer energy from one place to another without transferring matter
- Energy is transferred by the waves, but matter is not
- The direction of the motion of the wave is the direction of the energy transfer
- Travelling waves can be of two types:
- Mechanical Waves, which propagate through a medium and cannot take place in a vacuum
- Electromagnetic Waves, which can travel through a vacuum
- 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 (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 (λ) is the length of one complete oscillation measured from same point on two consecutive waves
- For example, two crests, or two troughs
- Measured in metres (m)
- Amplitude (x0) 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)
- Period (T) is the time taken for a fixed point on the wave to undergo one complete oscillation
- Measured in seconds (s)
- Frequency (f) is the number of full oscillations per second
- Measured in Hertz (Hz)
- Wave speed (c) is the distance travelled by the wave per unit time
- Measured in metres per second (m s-1)
Diagram showing the amplitude and wavelength of a wave
- The frequency, f, and the period, T, of a travelling wave are related to each other by the equation:
Period T and frequency f of a travelling wave
Worked example
The graph below shows a travelling wave.
Determine:
(i) The amplitude A of the wave in metres (m)
(ii) The frequency f of the wave in hertz (Hz)
(i) Identify the amplitude A of the wave on the graph
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- The amplitude is defined as the maximum displacement from the equilibrium position (x = 0)
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- The amplitude must be converted from centimetres (cm) into metres (m)
(ii) Calculate the frequency of the wave
Step 1: Identify the period T of the wave on the graph
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- The period is defined as the time taken for one complete oscillation to occur
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- 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
Step 3: Substitute the value of the period determined in Step 1
f = 1000 Hz