Transverse Pulses

Table of Contents
1. Introduction and key concepts
2. Pulses: definition, types and basic properties
3. Pulse speed
4. Investigations and classroom activities
5. Superposition and interference of pulses
6. Exercises and practice
7. End-of-chapter exercises (selected)
8. Summary of key points
9. Physical quantities and units
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Introduction and key concepts

When a disturbance moves through a substance without any bulk transport of the substance itself, we call that disturbance a pulse. Examples include the ripple produced when you touch the surface of water and the single hump produced on a rope when one end is flicked. The substance through which the pulse travels is called the medium.

What is a medium?

Medium - a medium is the substance or material in which a pulse moves. The medium transmits the disturbance from one place to another but does not itself travel along with the pulse. In a medium, particles are temporarily displaced from their equilibrium (rest) position and interact with neighbouring particles so that the disturbance propagates.

Pulses: definition, types and basic properties

What is a pulse?

Pulse - a pulse is a single disturbance that travels through a medium.

Transverse pulse

Transverse pulse - a pulse in which each particle of the medium is displaced perpendicular to the direction of travel of the pulse. For example, when a horizontally held rope is flicked up and down, the rope moves vertically while the pulse travels horizontally; this is a transverse pulse.

Pulse amplitude and pulse length

Amplitude (A) - the maximum displacement of the medium from its equilibrium (rest) position due to the pulse. Amplitude is measured in metres (m).

Pulse length (p) - a measure of how long (along the direction of propagation) the pulse is; it is the spatial extent of the disturbance at an instant.

Pulse speed

Pulse speed - the distance a pulse travels per unit time.

If a pulse travels a distance D in time t, its speed v is given by

v = D / t

Units: metre per second (m·s^-1).

Worked example: pulse speed

Investigations and classroom activities

Observation of pulses (rope experiment)

Activity: Stretch a heavy rope horizontally between two people. One person gives a quick upward flick at one end of the rope (a single flick). A single pulse travels along the rope away from the flicked end. Observe the direction of particle displacement and the direction of pulse propagation: they are at right angles for a transverse pulse.

Pulse length and amplitude - visual measurement

Activity: Using the rope or a measured diagram of a pulse at successive times, measure the pulse amplitude (A) and pulse length (p) at different instants. You will observe that, for an undistorted pulse travelling without dispersion, the amplitude and pulse length remain the same as the pulse moves (they are properties of the pulse and do not change just because the pulse has moved in the medium).

Superposition and interference of pulses

More than one pulse can occupy the same region of a medium at the same time. When this happens, the resulting displacement at any point is given by the principle of superposition.

Principle of superposition - when two or more disturbances occupy the same place in the medium at the same time, the resultant disturbance is the algebraic sum of the individual disturbances (sum of their displacements).

Important consequence: after the pulses pass through one another, each pulse continues on its original path and retains its original shape and amplitude (no permanent change to the pulses from the interaction if the medium is linear and there is no energy loss during the interaction).

Constructive interference

Constructive interference occurs when two pulses meet with displacements in the same direction (for example, two crests or two troughs). The resultant pulse has amplitude equal to the sum of the two amplitudes and is therefore larger in magnitude.

Destructive interference

Destructive interference occurs when two pulses meet with displacements in opposite directions (one a crest, the other a trough). The resultant displacement is the algebraic sum; if amplitudes are equal and opposite the pulses cancel completely at that instant. If magnitudes differ, a partial cancellation occurs and the resultant amplitude equals the difference between amplitudes, with sign determined by the larger amplitude.

Example: two pulses approaching each other

Situation: Two pulses A and B move towards each other along the same line at the same speed. To predict the waveform at later times, follow this method:

• Find how far each pulse moves in the given time: distance = speed × time.
• Shift the position of each pulse accordingly: pulse A in its direction of travel, pulse B in its direction.
• If the shifted pulses overlap at any location, add their displacements algebraically at those points to obtain the resultant wave (superposition).
• If they do not overlap, each pulse simply appears at its shifted position with original shape and amplitude.

After the interaction, when pulses have passed each other, each continues with its original shape and amplitude.

Class demonstration: ripple tank

Use a ripple tank to produce single pulses or pairs of pulses in water.

1. Set up the ripple tank with calm water.
2. Produce a single pulse (tap the water gently) and observe propagation.
3. Produce two pulses simultaneously from different points and observe interference.
4. Produce two pulses at slightly different times and observe partial constructive or destructive interference as they overlap.

Observation: Simultaneous pulses can show constructive interference; pulses produced at different times can show destructive or partial interference during overlap.

Exercises and practice

End-of-chapter exercises (selected)

1. A heavy rope is flicked upwards, creating a single pulse in the rope. Make a labelled drawing of the rope and indicate the following on your drawing:
   1. The direction of motion of the pulse.
   2. The direction of motion of the particles of the rope at the crest.
   3. The amplitude of the pulse.

Summary of key points

• A medium is the substance in which a pulse will move.
• A pulse is a single disturbance that moves through a medium.
• In a transverse pulse, particle displacement is perpendicular to the direction of pulse propagation.
• Amplitude is the maximum displacement from equilibrium; measured in metres (m).
• Pulse speed is distance travelled per unit time: v = D / t; units m·s^-1.
• Superposition-when pulses overlap, the net displacement is the algebraic sum of the individual displacements.
• Constructive interference produces a larger resultant pulse; destructive interference produces a smaller resultant pulse or cancellation.

Physical quantities and units