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E3.6 · Explain natural phenomena using wave properties

Learn to explain natural phenomena using wave properties through clear examples and targeted practice.

Ontario Grade 11 Physics

Waves and Sound

Reflection, refraction, diffraction, and interference

Waves can return from boundaries, change direction, spread through openings, and combine with other waves. These properties help explain echoes, the bending of water waves, sound heard around a corner, and places where sound is louder or quieter. In this lesson, the physical system is a wave travelling through a material and interacting with a boundary, an opening, or another wave. For a straight-line diagram, choose a positive direction, such as rightward. Wave travel has a direction, so velocity is a vector. Speed is the size of that velocity and is a scalar. Frequency, wavelength, and amplitude are also scalars. We use wave properties to explain what happens; a model or example is not a report of a physical measurement.

What you will learn

Describe waves using wavelength, frequency, amplitude, and speed.
Explain familiar natural phenomena using reflection, refraction, diffraction, and interference.
Use wave relationships to make predictions and check units and reasonableness.

1. Prerequisite bridge: describing a wave

A repeating wave has crests and troughs. A crest is a high point, and a trough is a low point. Wavelength, written as

\lambda

, is the distance between matching points on consecutive cycles, such as crest to crest. Wavelength is measured in metres (

\mathrm{m}

). It is a scalar distance and has no direction.

Frequency, written as

f

, is the number of complete cycles that pass a point each second. Its SI unit is the hertz (

\mathrm{Hz}

), equal to one cycle per second. Wave speed,

v

, tells how quickly the wave pattern travels through a material. It is measured in metres per second (

\mathrm{m/s}

). Amplitude is the greatest displacement from the undisturbed position. For sound, a greater amplitude is usually heard as greater loudness. Frequency is related to pitch, not loudness.

The relationship between wave speed, frequency, and wavelength is

v=f\lambda

. It describes the movement of the wave pattern, not the movement of the material as a whole. If a wave remains in one material and its speed stays constant, a higher frequency means a shorter wavelength.

v=f\lambda

Wavelength is a scalar distance; frequency counts cycles per second.
Wave velocity includes direction, while speed is its scalar magnitude.

2. Reflection and refraction

Reflection occurs when a wave reaches a boundary and returns into the material it came from. An echo is reflected sound. The sound travels away from its source, reflects from a surface, and travels back. This explains why a listener can hear a sound after the original sound has stopped.

Refraction is a change in a wave’s direction caused by a change in wave speed. A normal is an imaginary line perpendicular to a boundary. In a wave diagram, label the boundary, the normal, the direction of travel, and the regions on each side. If a water wave enters a slower region at an angle, it bends toward the normal. If it enters a faster region at an angle, it bends away from the normal.

The direction change happens because one part of a wave reaches the new region before another part does. The first part changes speed while the rest has not yet crossed. At the boundary, frequency remains the same. If speed changes, wavelength changes too, as shown by

v=f\lambda

. Refraction is not a wave bouncing back from the boundary.

v=f\lambda

Reflection returns a wave from a boundary and can produce an echo.
Refraction changes a wave’s direction when its speed changes between regions.

3. Diffraction and interference

Diffraction is the spreading of waves as they pass through an opening or around an obstacle. Sound can be heard around a doorway because sound waves spread through the opening. Spreading is especially noticeable when an opening is about the same size as the wavelength. It is less noticeable when the opening is much wider than the wavelength.

Interference occurs when waves overlap. At a point, their displacements combine. In constructive interference, crests line up with crests and troughs line up with troughs. The resulting displacement is greater. In destructive interference, a crest overlaps a trough, reducing the displacement. Equal and opposite displacements cancel at that point.

For two waves of the same frequency, the difference between the distances they travel to a point is called path difference. The path difference alone does not always determine the result: the waves’ relative phase when they are produced also matters. Phase describes where a wave is in its repeating cycle. If the sources start in phase, a whole-number wavelength path difference produces constructive interference. A path difference equal to half a wavelength plus a whole number of wavelengths produces destructive interference. This helps explain why sound from two sources can be louder in some places and quieter in others.

\Delta L=n\lambda

Diffraction is wave spreading at an opening or around an obstacle.
Interference can increase or reduce displacement, depending on how waves line up.
Use the path-difference rules only with the appropriate phase assumption.

4. Choosing a wave explanation

Begin with the observation. A returning sound suggests reflection. A wave changing direction as its speed changes suggests refraction. Spreading at an opening suggests diffraction. A pattern of louder and quieter sound from overlapping waves suggests interference.

Keep diagrams simple and labelled. Show the boundary or opening when it matters. Use arrows to show wave-velocity directions. For refraction, draw the normal. For interference, mark where crests and troughs meet. Choose a positive direction before describing travel and use it consistently. A reflected wave travels in the opposite direction from the incoming wave.

When using a calculation, list known values with units and identify the unknown. Choose a relationship that matches the situation. Keep units in substitutions, round to a sensible number of significant figures, and check that the answer’s units and size make sense. A wave model helps explain or predict a pattern; it is not automatically evidence from a physical investigation.

Match the wave property to the observation before choosing a relationship.
Check units, significant figures, direction where relevant, and physical reasonableness.

Worked example

Finding the wavelength of a sound wave

A sound wave travels through air at

340\ \mathrm{m/s}

and has a frequency of

425\ \mathrm{Hz}

. Find its wavelength.

Define the system and direction
The system is the sound wave travelling through air. Let rightward be the positive direction of travel. The given values are speed and frequency; the unknown is wavelength. Speed and frequency are scalars. The wave’s velocity would point rightward, but wavelength has no direction.
Choose the wave relationship
Wave speed equals frequency multiplied by wavelength. Rearranging for wavelength gives speed divided by frequency.
$\lambda=\frac{v}{f}$
Substitute and calculate
Use the given speed and frequency. A hertz is one cycle per second, so dividing metres per second by cycles per second gives metres per cycle, or metres for the wavelength.
$\lambda=\frac{340\ \mathrm{m/s}}{425\ \mathrm{Hz}}=0.800\ \mathrm{m}$

Answer: The wavelength is

0.800\ \mathrm{m}

. It is a scalar distance, so it has no direction.

Check: The units reduce to metres. A frequency of 425 cycles each second and a wavelength of 0.800 m give a wave speed of 340 m/s, so the result agrees with the given speed.

Worked example

Explaining a water wave changing direction

A water wave reaches a region where it travels more slowly. It meets the boundary at an angle. Explain what happens to its direction and wavelength.

Define the situation and direction
The system is the water wave crossing from the first region into the slower region. Take the direction toward the boundary as positive before the wave reaches it. The wave continues into the second region. The unknowns are the qualitative changes in direction and wavelength.
Use the wave-speed relationship
Wave speed, frequency, and wavelength are related. At the boundary, frequency stays the same. Therefore, a lower speed corresponds to a shorter wavelength.
$v=f\lambda$
Describe the direction change
Because the wave enters a slower region at an angle, it bends toward the normal. Its direction changes, while its frequency stays the same and its wavelength decreases.

Answer: The wave bends toward the normal and has a shorter wavelength in the slower region. Its frequency remains unchanged.

Check: This is a qualitative prediction, so no numerical rounding is needed. It is consistent with the wave-speed relationship: unchanged frequency and lower speed require a shorter wavelength.

Worked example

Predicting sound interference from path difference

Two sound sources start in phase and produce waves of the same frequency. The waves reach a listener with a path difference of

1.50\ \mathrm{m}

and a wavelength of

0.75\ \mathrm{m}

. Does the simple wave model predict constructive or destructive interference?

Define the system and known values
The system is the two sound waves reaching one listener. The sources start in phase, so they begin at the same point in their cycles. Path difference and wavelength are scalar distances. The known values are $\Delta L=1.50\ \mathrm{m}$ and $\lambda=0.75\ \mathrm{m}$ . The unknown is the type of interference predicted.
Compare path difference with wavelength
Divide the path difference by the wavelength. Metres cancel, leaving the number of wavelengths in the path difference.
$\frac{\Delta L}{\lambda}=\frac{1.50\ \mathrm{m}}{0.75\ \mathrm{m}}=2.0$
Interpret the result
The path difference is two whole wavelengths. Because the sources start in phase, the waves can arrive in step and reinforce one another.
$\Delta L=2\lambda$

Answer: The model predicts constructive interference because the sources start in phase and the path difference is two wavelengths.

Check: The ratio is dimensionless, as expected for a count of wavelengths. A whole-number wavelength difference preserves the in-phase alignment in this model.

Common mistakes and how to avoid them

Calling every change in wave direction reflection.

Correction: Reflection returns a wave from a boundary. Refraction changes direction because wave speed changes as the wave enters another region.

Saying diffraction is a wave bouncing around an obstacle.

Correction: Diffraction is the spreading of a wave at an opening or around an obstacle.

Assuming overlapping waves always make a larger wave.

Correction: Crests and troughs can combine to reduce displacement. The result depends on how the waves line up.

Changing frequency whenever a wave enters a new region.

Correction: In this refraction model, frequency stays the same at the boundary. Speed and wavelength change together.

Treating wavelength as a vector pointing in the direction a wave travels.

Correction: Wavelength is a scalar distance between matching points on cycles. The wave’s velocity has a direction.

Lesson summary

Reflection returns a wave from a boundary and can produce an echo.
Refraction changes wave direction when wave speed changes between regions.
Diffraction is spreading at an opening or around an obstacle.
Interference occurs when waves overlap; it can be constructive or destructive, depending on how the waves line up.
The relationship $v=f\lambda$ connects wave speed, frequency, and wavelength.

Check your understanding

Question 1

Which wave property best explains sound spreading through a doorway about the size of its wavelength?

Reflection
Diffraction
Constructive interference
Refraction

Show answer and explanation

Diffraction

Diffraction is the spreading of waves at openings. It is noticeable when an opening is comparable in size to the wavelength.

Question 2

A wave enters a slower region at an angle. In the qualitative refraction model, which way does it bend?

Toward the normal
Away from the normal
It always travels along the boundary
It must return to the first region

Show answer and explanation

Toward the normal

A wave entering a slower region at an angle bends toward the normal.

Question 3

Two sound sources start in phase and produce same-frequency waves. The waves reach a listener with a path difference of two wavelengths. What does the simple model predict?

Constructive interference
Destructive interference
Diffraction
Reflection

Show answer and explanation

Constructive interference

With sources starting in phase, a whole-number wavelength path difference can make the waves arrive in step, producing constructive interference.

Key terms

Amplitude: The greatest displacement of a wave from its undisturbed position.
Diffraction: The spreading of a wave as it passes through an opening or around an obstacle.
Frequency: The number of complete wave cycles passing a point each second.
Interference: The combining of wave displacements when waves overlap.
Normal: An imaginary line perpendicular to a boundary, used to describe wave directions and angles.
Path difference: The difference between the distances two waves travel to reach the same point.
Phase: A description of where a wave is in its repeating cycle.
Reflection: The return of a wave from a boundary into the material it came from.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation E3.6. 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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