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E3.1 · Distinguish longitudinal and transverse waves

Learn to distinguish longitudinal and transverse waves through clear examples and targeted practice.

Ontario Grade 11 Physics

Waves and Sound

Use the motion of the medium to identify the wave type

A wave can move through a material even though the material itself does not travel along with the wave. To describe the wave, keep track of two directions: the direction the wave travels and the direction parts of the material move as the wave passes. This lesson focuses on comparing those directions. A longitudinal wave has medium motion parallel to the wave’s travel direction. A transverse wave has medium motion perpendicular to it.

What you will learn

Define the system and choose directions before describing a wave.
Distinguish the direction a wave travels from the motion of the medium.
Classify waves as longitudinal or transverse using the relationship between those directions.
Use simple diagrams and examples to explain each classification.

1. Set up the description: system and directions

A system is the object or material you choose to study. For a wave on a rope, the system is the rope. For a sound wave in air, the system is the air through which the sound travels. The medium is the material that carries the wave, such as a rope or air.

Choose a reference frame before describing motion. A reference frame is the viewpoint used to say which way something moves. In the diagrams and examples here, view the medium from a fixed position. Choose the wave’s direction of travel as positive. For a wave travelling to the right, right is positive; up and down describe motion of the medium relative to its resting position.

A vector has both size and direction. The direction of motion of a piece of the medium can be described as a vector. A scalar has size but no direction. In this lesson, the key comparison is not how large the motions are. It is whether the medium’s motion points along the wave’s travel direction or across it.

A wave is a disturbance that travels through a medium. A disturbance is a change from the medium’s usual or resting state. A pulse is one short disturbance. A repeating series of disturbances can also form a wave. The wave travels from place to place; individual parts of the medium move around their own resting positions as the disturbance passes.

System: the material being studied.
Reference frame: the chosen viewpoint for describing motion.
Set positive as the wave’s direction of travel; state the medium’s motion separately.
Compare directions, not the distance travelled by the wave and by a piece of the medium.

2. The two wave types

For a longitudinal wave, parts of the medium move parallel to the direction the wave travels. Parallel means along the same line. The motion may point in the same or opposite direction at different moments, but it remains along that line. In a compressed spring, for example, coils bunch closer together and spread farther apart as the disturbance passes. Those changes travel along the spring, while the coils move back and forth along it.

For a transverse wave, parts of the medium move perpendicular to the direction the wave travels. Perpendicular means at a right angle. For a pulse travelling along a horizontal rope, a small piece of rope may move up and down while the pulse moves horizontally. The two directions are at right angles.

A simple labelled sketch can make the comparison clear. The arrow marked wave travel shows the direction the disturbance moves. The other arrow shows the direction the medium moves. Do not use the shape of the wave alone to decide its type; use the medium’s motion.

Wave diagrams often show a curved line. That line can show the shape of a disturbance along the medium at a moment. It does not, by itself, show the path followed by a piece of the medium. Look for the labels or description of the medium’s motion. If those are missing, the sketch may not provide enough information to classify the wave.

\text{longitudinal: medium motion }\parallel\text{ wave travel; transverse: medium motion }\perp\text{ wave travel}

Longitudinal: medium motion is parallel to wave travel.
Transverse: medium motion is perpendicular to wave travel.
A wave’s drawn shape alone does not always reveal how the medium moves.

3. Read and compare wave diagrams

Use the same directions consistently. In these sketches, right is the positive direction of wave travel. The system is the medium. Arrows marked “medium motion” show the motion of a small part of that medium as the wave passes. They do not show the direction the whole medium travels.

Longitudinal sketch: the wave travels to the right, and a small part of the medium moves back and forth horizontally. The motion is along the travel direction. Transverse sketch: the wave travels to the right, and a small part of the medium moves vertically. The motion is at a right angle to the travel direction.

The motion of the medium can reverse direction during a wave’s passage. That does not change the classification. A coil moving left and then right still moves along the spring. A rope segment moving up and then down still moves across the rope’s direction of wave travel.

This is a direction-based model, not a calculation. No numerical values or units are needed to decide whether the motion is parallel or perpendicular. If a problem gives a direction for travel and a direction for medium motion, compare them directly. If it gives only a name or a sketch, use the stated physical situation and check whether the relevant motion is described.

Use arrows to label wave travel and medium motion separately.
A change in the medium’s direction during the disturbance does not by itself change the wave type.
For this classification, direction is the relevant evidence; numerical measurement is not required.

4. Apply the distinction to familiar situations

A pulse travelling along a stretched rope is a useful transverse example when the rope moves up and down while the pulse moves along the rope. The rope is the system, and its segments move perpendicular to the pulse’s travel direction.

A sound wave travelling through air is a longitudinal example. Air particles move back and forth along the direction the sound travels. This description refers to the motion of the air, not to air being carried all the way from the source to the listener.

A slinky can show either type, depending on how the disturbance is made and which way it travels. Push and pull coils along the slinky’s length to make a longitudinal disturbance. Move the end sideways to make a transverse disturbance. These examples illustrate the direction comparison; they are not reports of measured results.

To classify any new example, name the medium, state the direction of wave travel, and state how a small part of the medium moves. Then compare the two directions. If they are along the same line, classify it as longitudinal. If they are at a right angle, classify it as transverse.

A rope pulse with up-and-down rope motion is transverse.
Sound in air is longitudinal because the air moves along the sound’s travel direction.
The same medium can illustrate different wave types when its motion is different.

Compare the directions

Wave type	Direction of medium motion compared with wave travel	Typical example in this lesson
Longitudinal	Parallel; along the same line	Sound travelling through air
Transverse	Perpendicular; at a right angle	A rope pulse with up-and-down rope motion

Worked example

A pulse on a rope

A pulse travels to the right along a horizontal rope. A marked point on the rope moves up and down as the pulse passes. Classify the wave.

Name the system and directions
The system is the rope. Use a fixed viewpoint, and choose right as the positive direction of wave travel. The marked point’s motion is vertical.
Compare the directions
The pulse travels horizontally, while the rope point moves vertically. These directions are at a right angle, so the wave is transverse.
$\text{horizontal wave travel}\perp\text{vertical medium motion}$

Answer: The pulse is a transverse wave.

Check: The classification depends on the rope point’s motion, not on the fact that the rope itself extends horizontally.

Worked example

Sound moving through air

A sound disturbance travels from left to right through air. The air moves back and forth from left to right as the disturbance passes. Classify the wave.

Name the system and directions
The system is the air. Use a fixed viewpoint and choose right as the positive direction of wave travel. The air’s back-and-forth motion is horizontal, along the same line as the sound’s travel.
Compare the directions
The air’s motion is parallel to the direction the sound travels. A wave with medium motion parallel to its travel direction is longitudinal.
$\text{air motion}\parallel\text{sound travel}$

Answer: The sound wave is longitudinal.

Check: The air moves back and forth locally; the description does not say that the same air travels from the source to the listener.

Worked example

A slinky disturbance

A student sends a disturbance along a slinky by moving its end sideways. A visible part of the slinky moves up and down while the disturbance travels along the slinky to the right. Classify the wave.

Identify the system
The system is the slinky. Choose right as the positive direction of wave travel. The stated motion of a part of the slinky is up and down.
Check the relationship
The slinky’s local motion is perpendicular to the disturbance’s direction of travel. The disturbance is therefore transverse.
$\text{medium motion}\perp\text{wave travel}$

Answer: The slinky disturbance is transverse.

Check: The classification follows from the described directions. It would not be enough to know only that the medium is a slinky.

Common mistakes and how to avoid them

Calling a wave transverse because its diagram is drawn as a wavy curve.

Correction: A curve shows a disturbance’s shape, not necessarily the path of the medium. Use the stated motion of a piece of the medium and compare it with wave travel.

Confusing motion of the wave with motion of the medium.

Correction: Label the two directions separately. The wave carries the disturbance along; the medium moves locally as the disturbance passes.

Thinking a medium must keep moving in one direction for the wave to have a type.

Correction: The medium can move back and forth. Classify the wave by whether that motion is along or at a right angle to wave travel.

Assuming every disturbance in the same material has the same type.

Correction: The type depends on the relationship between the medium’s motion and the wave’s travel direction. A slinky can illustrate either relationship.

Lesson summary

First name the system and choose a fixed viewpoint.
State the direction the wave travels and the direction a part of the medium moves.
Parallel medium motion means longitudinal; perpendicular medium motion means transverse.
Use the medium’s motion, not just a drawing’s shape, to classify a wave.
For this distinction, compare directions; no numerical calculation is needed.

Check your understanding

Question 1

A disturbance travels to the left along a rope. A point on the rope moves up and down. Which type is it?

Longitudinal, because the rope is the medium
Transverse, because the motions are perpendicular
Longitudinal, because the wave travels along the rope
It cannot be classified unless the speed is known

Show answer and explanation

Transverse, because the motions are perpendicular

The rope point moves vertically while the disturbance travels horizontally. The directions are perpendicular, so the wave is transverse.

Question 2

In a longitudinal wave, how does the medium move compared with the wave’s travel direction?

At a right angle to it
Along the same line as it
In a circle around it
The medium does not move at all

Show answer and explanation

Along the same line as it

Longitudinal waves have medium motion parallel to wave travel. The medium may move back and forth along that line.

Question 3

Air moves back and forth along the direction a sound disturbance travels. What type of wave is described?

Transverse, because air moves back and forth
Transverse, because sound travels through air
Longitudinal, because air motion is parallel to wave travel
It cannot be classified without measuring the air’s speed

Show answer and explanation

Longitudinal, because air motion is parallel to wave travel

The air’s motion is along the same line as the sound’s travel direction, so the wave is longitudinal.

Key terms

Medium: The material through which a wave disturbance travels.
System: The object or material chosen for study.
Reference frame: The viewpoint used to describe motion.
Disturbance: A change from a medium’s usual or resting state.
Pulse: One short disturbance that travels through a medium.
Parallel: Along the same line or in the same direction line.
Perpendicular: At a right angle.
Vector: A quantity described by both size and direction.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation E3.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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