A pulse is the simplest form of a wave — a single disturbance moving through a medium. In this chapter you will explore transverse pulses, understand what happens when two pulses meet (superposition), and discover the properties that describe all transverse waves.
1.1 Pulses and Transverse Pulses
Hold one end of a slinky spring on the floor while a friend holds the other end. Now give your end a single, sharp sideways flick — and watch what happens. A 'hump' of disturbance travels along the spring toward your friend. That hump is a pulse. Once the pulse has passed, every part of the spring returns to its resting position. A pulse is temporary — it is a single disturbance, not a continuous wave.
Definition
Medium
A substance or material along which a pulse moves. Examples: a rope, a slinky spring, water, or air.
Definition
Pulse
A pulse is a single disturbance that moves through a medium.
Definition
Transverse pulse
A pulse where all of the particles disturbed by the pulse move perpendicular (at a right angle) to the direction in which the pulse is moving.
The word TRANSVERSE means 'across' or 'at right angles'. In a transverse pulse, if the pulse moves horizontally (→), the particles of the medium move vertically (↑↓). These two directions are perpendicular (90°) to each other. This is the defining feature of all transverse disturbances.
Definition
Amplitude (A)
The amplitude of a pulse is the maximum disturbance or distance the medium is displaced from its rest (equilibrium) position.
Watch Out
COMMON MISTAKE — Amplitude is NOT the total height of the pulse (from the lowest to the highest point). It is the distance from the equilibrium (rest) position to the peak of the pulse only. For a pulse that only rises above the equilibrium line, amplitude = height of the peak above the line.
Real World
EXPERIMENT: Generate a transverse pulse in a slinky. Fasten a ribbon to one of the coils so you can track a single particle. Observe that the ribbon moves sideways (perpendicular) while the pulse moves along the slinky. This confirms the definition of a transverse pulse.
1.2 Superposition of Pulses
What happens when two pulses travelling towards each other on the same rope actually meet? Do they crash into each other and stop? Does the bigger one 'win'? The answer is: for a brief moment they OVERLAP, and the medium takes on a shape that is the COMBINATION of both pulses. After the overlap, each pulse continues as if nothing happened. This behaviour is described by the principle of superposition.
Definition
Principle of superposition
The principle of superposition states that when two disturbances occupy the same space at the same time the resulting disturbance is the sum of two disturbances.
CONSTRUCTIVE INTERFERENCE happens when both pulses are on the SAME SIDE of the equilibrium position (both above, or both below). Their displacements ADD together. If pulse P has amplitude 4 cm (above) and pulse Q has amplitude 3 cm (also above), the combined pulse at the moment of overlap has amplitude 4 + 3 = 7 cm. The result is BIGGER than either pulse on its own.
Definition
Constructive interference
Constructive interference is when two pulses meet, resulting in a bigger pulse.
DESTRUCTIVE INTERFERENCE happens when the two pulses are on OPPOSITE SIDES of the equilibrium position (one above, one below). Their displacements SUBTRACT. If pulse P has amplitude 5 cm (above) and pulse Q has amplitude 5 cm (below), the result at the moment of overlap is 5 − 5 = 0 cm. The medium appears completely FLAT for that instant — as if there were no pulse at all.
Definition
Destructive interference
Destructive interference is when two pulses meet, resulting in a smaller pulse.
Note
KEY INSIGHT — After superposition (whether constructive or destructive), each pulse CONTINUES in its original direction with its ORIGINAL shape and amplitude. The pulses do NOT stop, bounce back, or permanently alter each other. Superposition is a temporary effect that only exists at the moment of overlap.
Exam Tip
EXAM TIP — For partial destructive interference (unequal amplitudes): resultant amplitude = A_larger − A_smaller, and the resultant pulse is on the same side as the larger pulse.
Worked Example
Two pulses travel toward each other on a string. Pulse A has amplitude 6 cm and is above the equilibrium. Pulse B has amplitude 2 cm and is above the equilibrium. (a) What type of interference occurs? (b) What is the resultant amplitude?
Given
- Amplitude of A: A_A = 6 cm (above equilibrium)
- Amplitude of B: A_B = 2 cm (above equilibrium)
Find
(a) Type of interference (b) Resultant amplitude
Solution
- 1Both pulses are on the SAME side of the equilibrium (both above) → constructive interference.
- 2Resultant amplitude = A_A + A_B
- 3= 6 + 2 = 8 cm
Worked Example
Pulse C has amplitude 9 cm above the equilibrium. Pulse D has amplitude 4 cm BELOW the equilibrium. (a) What type of interference occurs when they meet? (b) What is the resultant amplitude and on which side of the equilibrium is it?
Given
- A_C = 9 cm (above equilibrium, positive)
- A_D = 4 cm (below equilibrium, negative)
Find
(a) Type of interference (b) Resultant amplitude and position
Solution
- 1Pulses are on OPPOSITE sides of the equilibrium → destructive interference.
- 2Resultant amplitude = A_C − A_D = 9 − 4 = 5 cm
- 3The resultant is on the same side as the larger pulse (above equilibrium).
Practice Question
A pulse X has amplitude 10 cm and is below the equilibrium line. A pulse Y has amplitude 10 cm and is above the equilibrium line. (a) State the type of interference. (b) Calculate the resultant displacement at the moment of overlap. (c) After they have passed through each other, describe the shape of each pulse.
(6 marks)
1.3 Transverse Waves and Their Properties
A single flick of a rope creates a pulse. But if you continuously flick the rope up and down at a steady rhythm, you create a continuous, repeating pattern of disturbances — this is called a WAVE. A wave is produced by a vibrating source. Every wave has a characteristic repeating shape (its waveform), and you can measure several important properties from it.
Definition
Transverse wave
A transverse wave is a wave where the movement of the particles of the medium is perpendicular (at a right angle) to the direction of propagation of the wave.
Definition
Crest
A crest is a point on the wave where the displacement of the medium is at a maximum.
Definition
Trough
A point on the wave is a trough if the displacement of the medium at that point is at a minimum.
Definition
Amplitude (A)
The amplitude of a pulse is the maximum disturbance or distance the medium is displaced from its rest (equilibrium) position.
Definition
Wavelength (λ)
The wavelength of a wave is the distance between any two adjacent points that are in phase.
Because the wavelength is the distance between two ADJACENT in-phase points, you can measure it as: crest to crest, trough to trough, or any two corresponding points one full cycle apart. These measurements all give the same value.
Definition
Period (T)
The period is the time taken for two successive crests (or troughs) to pass a fixed point.
Definition
Frequency (f)
The frequency is the number of successive crests (or troughs) passing a given point in 1 second.
Note
SI UNITS: Wavelength λ → metres (m). Period T → seconds (s). Frequency f → hertz (Hz), where 1 Hz = 1 cycle per second = 1 s⁻¹. Amplitude A → metres (m) or centimetres (cm).
Definition
Points in phase
Two points in phase are separated by a whole (1, 2, 3, …) number multiple of whole wave cycles or wavelengths.
Definition
Points out of phase
Points that are not in phase, those that are not separated by a complete number of wavelengths, are called out of phase.
HOW TO IDENTIFY WAVE PROPERTIES ON A DIAGRAM: • Crests = highest points • Troughs = lowest points • Amplitude = vertical distance from equilibrium line to a crest (measure upward) • Wavelength (λ) = horizontal distance from one crest to the NEXT crest • Two crests → in phase | Crest + adjacent trough → out of phase (½λ apart) • Two points at same height moving in same direction → in phase
Practice Question
A transverse wave has a wavelength of 6 m. (a) What is the distance between adjacent crests? (b) What is the distance between a crest and the next trough? (c) Are the first and third crests in phase? Explain. (d) Are a crest and the adjacent trough in phase? Explain.
(6 marks)