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E1.1 · Analyse how wave properties influence structures and devices

Learn to analyse how wave properties influence structures and devices through clear examples and targeted practice.

Ontario Grade 11 Physics

Waves and Sound

How wave properties affect what structures and devices do

Waves transfer energy from place to place. Their properties help explain why a bridge can vibrate, why a sound barrier works better for some sounds than others, and how a device can use a reflected wave to detect an object. This lesson focuses on those connections. A wave can travel in a material medium, such as air or water, or through space. In each example, the system is the wave and the structure or device that interacts with it. When a direction is needed, positive is the direction the wave initially travels. Frequency, wavelength, amplitude, and speed are scalar quantities: each has a size but no direction. Wave travel direction is shown separately.

What you will learn

Describe how frequency, wavelength, amplitude, and wave speed affect waves.
Explain how reflection, absorption, and resonance can affect structures and devices.
Use the relationship between wave speed, frequency, and wavelength to make and check a prediction.

1. Prerequisites: describing a wave

A repeating wave has crests, the highest points, and troughs, the lowest points. Wavelength, written as

\lambda

, is the distance between matching points on neighbouring waves, such as crest to crest. Its SI unit is the metre (

\mathrm{m}

). Frequency, written as

f

, is the number of complete wave cycles that pass a point each second. It is measured in hertz (

\mathrm{Hz}

), where

1\ \mathrm{Hz}=1\ \mathrm{s^{-1}}

Amplitude is the maximum distance a point on the wave moves from its resting position. It is measured in metres for a displacement wave. A larger amplitude means the wave carries more energy in many familiar situations, but amplitude alone does not tell us how quickly the wave repeats. Wave speed,

v

, is the distance the wave travels per second, measured in metres per second (

\mathrm{m/s}

The wave relationship connects these properties. It applies when the wave speed is known for its medium and conditions. Changing frequency in the same medium generally changes wavelength so that the relationship remains true.

v=f\lambda

Frequency describes how often cycles pass; wavelength describes their spacing.
Amplitude describes the size of the disturbance.
Wave speed depends on the wave and the medium.

2. When waves meet structures

A structure can reflect, absorb, transmit, or vibrate in response to an incoming wave. Reflection occurs when a wave bounces back from a boundary. Absorption occurs when some wave energy is taken in by a material, often becoming thermal energy. Transmission occurs when a wave passes through a material. These effects depend on the wave and on the structure's material, shape, and size.

A building wall may reflect some sound and absorb other sound. Soft, porous materials often absorb more sound than a hard, smooth surface. A sound barrier can reduce sound reaching an area behind it, but sound can also bend around an edge. This bending is called diffraction. Diffraction is more noticeable when the wavelength is similar to the size of an opening or obstacle. Because low-frequency sound usually has a longer wavelength than high-frequency sound in the same air, it may bend around a barrier more readily.

Waves can also make a structure vibrate. Resonance is a large response that can occur when repeated pushes arrive at a frequency close to the structure's natural frequency. A natural frequency is a frequency at which an object tends to vibrate. Repeated small pushes can then add energy to the vibration. Engineers consider this possibility when designing structures and devices. Damping is a process that reduces vibration by removing energy from it, for example through materials or connections that turn some vibration energy into heat.

Reflection, absorption, transmission, and diffraction affect how much wave energy reaches a place.
A structure may respond strongly when the wave frequency is close to its natural frequency.
Damping reduces vibration; it does not change the definition of frequency or wavelength.

3. Devices that use wave behaviour

Devices are designed around the wave properties that suit their purpose. A sonar device sends sound through water and detects sound reflected from an object. Its operation depends on sound travelling through the water and returning to the device. A microphone converts sound vibrations into an electrical signal. Soundproofing materials aim to absorb or block sound, while an acoustic reflector is shaped to direct reflected sound toward a chosen area.

A device may also select or reduce particular frequencies. For example, a sound system can be designed to reduce unwanted frequency ranges. The design matters because different frequencies have different wavelengths in the same medium, and structures with different sizes can interact with them differently.

To analyse a wave-related design, identify the wave and its medium, note the relevant property, and explain how the structure or device responds. If a calculation is needed, state the known quantities and the unknown. Use SI units, keep units in the substitution, and check whether the result fits the situation.

A wave-based device uses a wave's travel, reflection, or frequency to perform a task.
The same structure can affect different wavelengths differently.
A useful explanation links a named wave property to a specific design effect.

4. Applying the model carefully

Before calculating, define the physical system. For a sound wave in air, the system can be the sound wave travelling through the air toward a barrier. Set positive direction as the direction the sound initially travels. This convention keeps the description clear, even though frequency, wavelength, and speed in

v=f\lambda

are scalar magnitudes and are not assigned positive or negative signs.

Use the relationship only with consistent units. If frequency is in hertz and wavelength is in metres, their product has units of metres per second. A sensible answer should also match the context: sound speed in air is hundreds of metres per second, not a few metres per second or millions of metres per second.

A calculation can support an analysis, but it does not by itself prove how well a real structure works. Actual performance depends on details such as the material, shape, and conditions. A proposed test or computer model can help investigate a design, but it should not be described as measured evidence unless measurements were actually made.

[v]=\mathrm{m/s},\quad [f]=\mathrm{Hz},\quad [\lambda]=\mathrm{m}

Define the system, medium, positive direction, known values, and unknown.
Check units and compare the result with a reasonable scale.
Separate a prediction from evidence gathered by measurement.

Worked example

Finding the wavelength of sound

A sound wave travels through air at

340\ \mathrm{m/s}

and has a frequency of

680\ \mathrm{Hz}

. Find its wavelength.

Define the system and direction
The system is the sound wave travelling through air. Positive is the direction the sound initially travels. The known values are speed and frequency; wavelength is unknown.
Choose the relationship
For a wave, speed equals frequency multiplied by wavelength. Rearrange to find wavelength.
$\lambda=\frac{v}{f}$
Substitute with units
Use the given SI values. The units reduce to metres because metres per second are divided by cycles per second.
$\lambda=\frac{340\ \mathrm{m/s}}{680\ \mathrm{Hz}}=0.50\ \mathrm{m}$

Answer: The wavelength is

0.50\ \mathrm{m}

, to two significant figures.

Check: The units are metres, as required for wavelength. The value is reasonable: at

340\ \mathrm{m/s}

, a frequency of

680\ \mathrm{Hz}

gives two cycles per metre. The positive direction is the sound's initial travel direction; wavelength itself is a scalar.

Worked example

Assessing a possible resonance concern

A structure has a natural frequency of

2.4\ \mathrm{Hz}

. A repeating force from a device acts at

2.3\ \mathrm{Hz}

. Explain whether resonance is a concern, and identify one suitable design response.

Define the system and direction
The system is the structure and the repeated force acting on it. The comparison is between two frequencies, which are scalar quantities. Direction is not needed to compare their sizes.
Compare the frequencies
The applied frequency is close to the structure's natural frequency. This means resonance may produce a stronger vibration, so the design should treat it as a concern. The comparison identifies a risk; it does not establish the size of an actual vibration.
$|2.4\ \mathrm{Hz}-2.3\ \mathrm{Hz}|=0.1\ \mathrm{Hz}$
Connect the analysis to design
A designer could change the structure so its natural frequency is farther from the repeated force frequency, or add damping to reduce vibration. The best choice depends on the structure and its use.

Answer: Resonance is a concern because the frequencies are close. Changing the structure's natural frequency or adding damping could reduce the response.

Check: Both values use hertz, so the comparison is consistent. The frequency difference is

0.1\ \mathrm{Hz}

, which is small compared with either frequency. This supports a concern, but does not predict an exact vibration amplitude.

Worked example

Considering sound near a barrier

Sound travels through air at

340\ \mathrm{m/s}

. Compare the wavelengths of a

170\ \mathrm{Hz}

sound and a

1700\ \mathrm{Hz}

sound. Which is more likely to bend around a barrier with an opening about

1.0\ \mathrm{m}

wide?

Define the system and direction
The system is each sound wave travelling through air toward the barrier. Positive is toward the barrier. The speed is the same for both sounds; wavelength is unknown in each case.
Calculate both wavelengths
Use the wave relationship and divide speed by frequency. Keep metres per second and hertz in each substitution.
$\lambda_{170}=\frac{340\ \mathrm{m/s}}{170\ \mathrm{Hz}}=2.0\ \mathrm{m},\quad \lambda_{1700}=\frac{340\ \mathrm{m/s}}{1700\ \mathrm{Hz}}=0.20\ \mathrm{m}$
Relate wavelength to the opening
The $170\ \mathrm{Hz}$ wave has a wavelength closer to the opening size. Diffraction is more noticeable when wavelength and opening size are similar, so this lower-frequency sound is more likely to bend around the barrier.

Answer: The wavelengths are

2.0\ \mathrm{m}

and

0.20\ \mathrm{m}

. The

170\ \mathrm{Hz}

sound is more likely to bend around the approximately

1.0\ \mathrm{m}

opening.

Check: Both answers have units of metres and are to two significant figures. The lower frequency gives the longer wavelength at the same speed, as expected. The conclusion is a comparison, not a claim that the barrier blocks none of either sound.

Common mistakes and how to avoid them

Treating frequency and wavelength as the same property.

Correction: Frequency is cycles per second; wavelength is the distance between matching points on neighbouring cycles.

Assuming a barrier blocks every frequency equally.

Correction: Different wavelengths can interact differently with an opening, an edge, and the barrier material.

Calling every large vibration resonance.

Correction: Resonance is a strong response that can occur when a repeated input frequency is close to a structure's natural frequency.

Saying that a calculated prediction is a measured result.

Correction: A calculation or model gives a prediction. Call something measured evidence only when measurements have actually been taken.

Lesson summary

Wave speed, frequency, and wavelength are linked by $v=f\lambda$ .
Reflection, absorption, transmission, and diffraction influence how waves interact with structures and devices.
A structure may vibrate strongly when a repeated input is close to its natural frequency; damping can reduce vibration.
Analyse a design by connecting a specific wave property to a likely effect, then check units, direction, and reasonableness.

Check your understanding

Question 1

In the same medium, what happens to wavelength when frequency increases and wave speed stays the same?

Wavelength increases.
Wavelength decreases.
Wavelength stays the same in every case.
correctIndex":1,"explanation":"Since $v=f\lambda$ and speed is fixed, a larger frequency requires a smaller wavelength."}

Show answer and explanation

Wavelength decreases.

Since

v=f\lambda

and speed is fixed, a larger frequency requires a smaller wavelength.

Question 2

A structure is driven by a repeating input close to its natural frequency. Which statement best describes the concern?

The structure may vibrate more strongly.
The wave must stop travelling.
The structure's wavelength becomes its natural frequency.
correctIndex":0,"explanation":"A repeated input near the natural frequency can produce resonance and a stronger vibration."}

Show answer and explanation

The structure may vibrate more strongly.

A repeated input near the natural frequency can produce resonance and a stronger vibration.

Question 3

Which sound is generally more likely to diffract around an opening when both travel through the same air?

A higher-frequency sound with a shorter wavelength.
A lower-frequency sound with a longer wavelength.
Both must diffract by exactly the same amount.
correctIndex":1,"explanation":"Diffraction is more noticeable when the wavelength is similar to the opening or obstacle size. Lower-frequency sound has a longer wavelength in the same medium."}

Show answer and explanation

A lower-frequency sound with a longer wavelength.

Diffraction is more noticeable when the wavelength is similar to the opening or obstacle size. Lower-frequency sound has a longer wavelength in the same medium.

Key terms

Amplitude: The maximum displacement of a point on a wave from its resting position.
Diffraction: The bending or spreading of a wave around an edge or through an opening.
Damping: A process that reduces vibration by removing energy from the vibrating system.
Frequency: The number of complete wave cycles passing a point each second, measured in hertz.
Natural frequency: A frequency at which an object tends to vibrate.
Resonance: A strong response that can occur when a repeated input is close to an object's natural frequency.
Wavelength: The distance between matching points on neighbouring cycles of a wave.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation E1.1. 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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