Graphs of Transverse & Longitudinal Waves
Graphs of Transverse Waves
- There are two common graphs transverse waves;
- Displacement against distance
- Displacement against time
- These are:
- Similar because they produce a sinusoidal shaped curve
- Different because displacement against distance is showing displacement of a point on the wave, but displacement against time is showing the wave itself moving along a line
- On the displacement-distance graph:
- Movement upwards from the centre line is given a positive sign and movement downwards a negative
- The amplitude and wavelength can be found as shown below
- On the displacement-time graph:
- The time period can be taken directly as shown
- This means that frequency can be found indirectly as f = 1/T
- To determine the next position of a point on the wave
- Sketch the full wave after time has passed by looking at the direction of travel
- Each point oscillates perpendicular to the wave, so remains on the normal line wherever the wave intersects, this is shown in red below
Graphs of Longitudinal Waves
- Plotting displacement against distance also produces a sinusoidal shaped graph
- This can be used to show where the compressions and rarefactions will be found
Worked Example
The graph shows how the displacement of a particle in a wave varies with time.
Which statement is correct?
A. The wave has an amplitude of 2 cm and could be either transverse or longitudinal.
B. The wave has an amplitude of 2 cm and has a time period of 6 s.
C. The wave has an amplitude of 4 cm and has a time period of 4 s.
D. The wave has an amplitude of 4 cm and must be transverse.
ANSWER: A
Graphs of Stationary Waves
- Stationary waves occur when a wave is reflected with a 180o phase difference, creating a wave with a series of nodes and antinodes
- Stationary waves can be transverse or longitudinal
- They are represented graphically in the same way as progressive (travelling) waves
- Graphs of standing waves can also be used to determine the position of nodes and antinodes
- L is the length of the string
- 1 wavelength λ is only a portion of the length of the string
Exam Tip
Both transverse and longitudinal waves can look like transverse waves when plotted on a graph - make sure you read the question and look for whether the wave travels parallel (longitudinal) or perpendicular (transverse) to the direction of travel to confirm which type of wave it is.
