Transverse Pulses
Grade 10
1. Pulses and Amplitude
A medium is the substance a pulse or a wave travels through, such as a rope, a spring or water. Hold a long rope still, flick one end up and down once, and a single hump travels along the rope. That hump is a pulse.
Definition: pulse
A pulse is a single disturbance in a medium.
A pulse happens only once. It has an amplitude and a pulse length, but it has no frequency, because it does not repeat.
Definition: transverse pulse
A transverse pulse is a pulse in which the particles of the medium move at right angles to the direction of propagation of the pulse.
A transverse pulse moving to the right. Each particle of the rope moves up and then down again, at right angles to the direction of propagation, and returns to its rest position.
The rope does not travel with the pulse
The particles of the medium only move up and down around their rest positions. What travels along the rope is energy, not the rope itself.
Definition: amplitude
Amplitude is the maximum disturbance of a particle from its rest (equilibrium) position.
The rest position is where the rope lies when no pulse is present. Amplitude is measured from the rest position to the highest point of an upward pulse, or to the lowest point of a downward pulse. The pulse length is the distance along the medium that the pulse takes up.
Measure amplitude from the rest position
Amplitude is not measured from the top of one pulse to the bottom of another. On a grid, count the squares from the rest position and multiply by the size of one square.
Which way is a particle moving?
For an upward pulse, particles in front of the peak (on the side the pulse is moving towards) are moving upwards, because the peak has not reached them yet. Particles behind the peak are moving downwards, back to rest.
Worked Examples
- 1Read the diagram:
- 2Amplitude: from the rest position to the peak is 5 squares. 5 × 0,5 cm = 2,5 cm.
- 3Pulse length: the pulse takes up 8 squares along the rope. 8 × 0,5 cm = 4 cm.
- 1Read the diagram:
- 2P is in front of the peak. The peak is still coming towards P, so P is moving upwards.
- 3Q is behind the peak. The peak has already passed Q, so Q is moving downwards, back to its rest position.
- 1In a transverse pulse the particles of the rope move at right angles to the direction the pulse travels.
- 2Each particle moves up, then down again, and returns to its rest position.
- 3Energy travels along the rope, but the rope itself stays where it is.
2. Superposition of Pulses
When two pulses travelling towards each other on the same rope meet, they occupy the same space at the same time. At that moment the displacement of the rope at each point is found by adding the displacements of the two pulses. This is the principle of superposition: superposition is the sum of the disturbances of the two pulses.
Definition: principle of superposition
The principle of superposition states that when two pulses occupy the same space at the same time, the resulting disturbance is the sum of the disturbances of the individual pulses.
Count upward displacements as positive and downward displacements as negative, then add them.
Definition: constructive interference
Constructive interference is the phenomenon where two pulses on the same side of the rest position overlap to produce a pulse of greater amplitude.
Before: pulse A (2 squares high) and pulse B (3 squares high) move towards each other.
Overlap: the dashed lines show A and B; the rope (solid) is their sum, 2 + 3 = 5 squares high.
After: A and B have passed through each other, unchanged.
Definition: destructive interference
Destructive interference is the phenomenon where two pulses on opposite sides of the rest position overlap to produce a pulse of smaller amplitude.
Before: pulse A (3 squares up) and pulse B (2 squares down) move towards each other.
Overlap: the rope is the sum, 3 + (−2) = 1 square upwards.
After: A and B continue with their original shapes.
Pulses are not destroyed when they meet. After overlapping, the pulses pass through each other and continue in their original directions with their original amplitudes and shapes.
Complete destructive interference
If two pulses of equal amplitude on opposite sides of the rest position overlap exactly, the displacements cancel and the rope is flat at that instant. A moment later both pulses appear again and move apart.
Directions matter
A 5 cm upward pulse and a 2 cm downward pulse give 3 cm upwards, not 7 cm. Only pulses on the same side of the rest position add up to a bigger pulse.
Demonstration: superposition of pulses
Send a pulse from each end of a stretched slinky spring (or a long rope) at the same time. Where two crests meet, they add up to a bigger pulse for a moment (constructive interference); where a crest meets a trough of the same size, they cancel (destructive interference). After they meet, each pulse carries on unchanged. Two pulses of water in a ripple tank show the same.
How to plan, record and write up a practical: see the scientific investigation skills guide.
Worked Examples
- 1Both pulses are on the same side of the rest position, so this is constructive interference.
- 2Add the displacements: 4 cm + 3 cm = 7 cm.
- 1The pulses are on opposite sides of the rest position, so this is destructive interference.
- 2Take upwards as positive: (+5 cm) + (−2 cm) = +3 cm.
- 1Read the diagram:
- 2At P both pulses are present: 3 squares up and 2 squares down. 3 + (−2) = 1 square, so 1 cm upwards.
- 3At Q only the upward pulse is present: 3 squares, so 3 cm upwards.
- 1Superposition only changes the displacement while the pulses overlap.
- 2After passing, each pulse continues in its original direction with its original amplitude and shape.