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# 4.3. Wave Characteristics

Waves can do some pretty cool stuff that make them super interesting to study. This section begins to explore some of these cool characteristics. Polarisation is extensively used in photography to reduce reflections and glare, exploiting some of the characteristics unique to transverse waves. Superposition is the result of two waves combining to produce either a larger amplitude or to cancel out. The Mythbusters team investigated the latter of these to see if shockwaves from two explosions equal distances away might be able to cancel each other out - take a look to see what happened.

Again, a lot of these concepts introduce here become much more significant later on, but the section has been divided up as follows:

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• Wavefronts and Rays - Different ways we can represent waves pictorially

• Superposition - Exploring the effects of exploring multiple waves

• Polarisation - A unique characteristic of transverse waves, with some cool applications

Wavefronts and Rays

#### Wavefronts and Rays

Wave diagrams are important pictorial representations of wave motion, and can be very useful in looking at the ideas of reflection, refraction and diffraction which come later.

The below diagrams have been taken from the PHET Refraction simulation. They show different representations of the same wave - on the left we see the light ray, on the right we see the same wave represented as wave fronts.

Here we see a gif representation of waves propagating from a point source. You can clearly see the wave fronts being emitted - these represent successive peaks, as if getting a birds-eye view of water waves washing up on a beach. The wavelength can be measured as the distance between successive wave fronts.

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The dotted red line represents one possible ray (being refracted). Note that the rays and wave fronts are always perpendicular.

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Wave fronts can be very useful tools in explaining many different ideas to do with wave properties. Isaac Physics have a decent online lesson on Huygens Principle, which makes use of wave fronts.

Falstad have an excellent simulation of a ripple tank. This is a really clear illustration of  wavefronts, and can also be used to demonstrate some important wave properties - reflection, refraction, diffraction etc.

## Resources

 IB Physics Topic 4 Notes IB-Physics.net Chapter 4 Summary IB Revision Notes Mr. G 4.3 Teaching Notes 4.3 Student Notes Physics and Maths Tutor Waves Definitions Waves Key Points Waves Detailed Notes Waves Progressive & Standing Waves A Level Resources - content slightly different

## Questions

 Cambridge University Press Topic 4: Add Qs Topic 4: Add Qs MS Topic 4: MCQs CUP Website Link Freely available online Grade Gorilla Topic 4 (Waves A) End Quiz Quick IB Specific Mixed MCQs Mr. G 4.3 Formative Assessment Topic 4 Summary Qs IB Specific Questions
Superposition

#### Superposition

Until now we have looked at individual waves in isolation. When multiple waves come together they will interact, and produce a resulting wave that is the superposition of the individual waves (i.e. adding together the displacements at each point). The phenomenon of interference is exploited by noise cancelling headphones to remove the ambient sounds of the environment (using superposition of waves to 'cancel out' the sound waves). This video describes how this is done.

## Principle of Superposition

When two (or more) waves meet, they interfere and create a superposition of the two waves. This is a characteristic property of wave behaviour. The Principle of Superposition states that:

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When two or more waves cross at a point, the displacement at that point is equal to the sum of the displacements of the individual waves.

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This is shown below with two pulses of the green wave interacting. As they pass through one another, their displacements add together to form a larger displacement when the two pulses are on top of one another.

The above is an example of something called constructive interference. That is the two waves both have positive displacements, so the vector sum produces a larger displacement as they pass through each otehr. We can also have  destructive interference, if one wave has a positive displacement and the other a negative displacement, the vector sum of the displacements will be smaller than the individuals. Isaac Physics have an online lesson on this topic that explains these ideas in more depth.

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The below gif illustrates this more clearly.

• Constructive Interference : When the blue and green wave are in phase (Φ = 0 radians), the superposition of the two waves (shown in red) has double the displacement of the individual components.

• Destructive Interference : When the blue and green wave are in antiphase (Φ = π radians), the superposition of the two waves (shown in red) has zero displacement, as the individual components 'cancel out'.

You can explore the relationship between phase difference and superposition further through this  Geogebra simulation. These ideas of superposition are characteristic of wave behaviour, and we will later explore why the fact that light follows some of these characteristics is so significant.

## Intensity and Amplitude

We just discussed how multiple waves can superpose to cause an increase or decrease in amplitude.

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Here we introduce a new quantity, Intensity, that measures the amount of energy in a certain wave.

We will explore this equation a bit later, in Chapter 8. The important thing to understand here, is how does intensity link to amplitude. If we have constructive superposition, and the amplitude of our wave doubles, the intensity of our wave goes up by a factor of 4 - i.e. A². This gives the following relationship:

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Intensity ∝ Amplitude²

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The intensity of a wave follows an inverse square relationship. We will encounter this later one when looking at gravitational and electric fields. If we have a point source of a wave (e.g. a small lightbulb), with the light propagating outwards, the intensity will decrease with the square of the distance (i.e. if I double the distance, the intensity decreases by a factor of 4; triple the distance the intensity decreases by a factor of 9).

## Video Lessons

 Chris Doner Superposition and Interference IB Specific Gradepod Principle of Superposition IB Specific Khan Academy Constructive & Destructive Interference Wave Interference Physics Online Superposition Phase vs Path Difference Study Nova Interfernce Interference (Lecture)

## Resources

 IB Physics Topic 4 Notes IB-Physics.net Chapter 4 Summary IB Revision Notes Isaac Physics Superposition Mr. G 4.3 Teaching Notes 4.3 Student Notes Physics and Maths Tutor Waves Definitions Waves Key Points Waves Detailed Notes Waves: Diffraction, Refraction, Interference A Level Resources - content slightly different

## Questions

 Cambridge University Press Topic 4: Add Qs Topic 4: Add Qs MS Topic 4: MCQs CUP Website Link Freely available online Grade Gorilla 4.3/4 (Interference) MCQ Topic 4 (Waves B) End Quiz Quick IB Specific Mixed MCQs Isaac Physics Path Difference Mixed Questions Mr. G 4.3 Formative Assessment Topic 4 Summary Qs IB Specific Questions
Polarisation

#### Polarisation

Transverse waves have a displacement that is perpendicular to the direction of energy transfer. However, in 3-dimensions, this displacement could be in any plane around 360 degrees. Polarising filters are able to selectively filter out some of these components such that only oscillations in a certain plane are able to pass through.

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Polarisation can only occur with transverse waves (e.g. light), because of these multiple planes of oscillation. Longitudinal waves (e.g. sound) all oscillate in the same direction as the energy transfer (so do not have the same 360° plane of oscillation), so they cannot be polarised.

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The below gif from Baumer illustrates this effect. Note that the orientation of the polarising filter only allows components in a vertical orientation to pass through. The transmitted orange wave will have 50% of the intensity of the unpolarised light entering the polarising filter.

Polarising filters can be used to reduce glare from water and snow. When reflected from these surfaces, the light becomes partially polarised. Polarising filters can therefore reduce the amount of light reflected from the surface entering the lens.

A Level Physics Online explains a few of the key ideas to do with polarisation below, and demonstrates the effects of rotating polarising filters.

## Malus' Law

Malus' Law is a mathematical description of the amount of light transmitted when passing through a polarising filter at an angle. If we use polarised light, the maximum amount of light will be transmitted at 0° or 180°, with zero intensity at 90°. This gives us a 'cosine' relationship (thinking about the cos graph).

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Malus' Law shows us how much light is transmitted when passing through a polarising filter and is shown below.

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Important point - when UNPOLARISED light passes through a filter, the transmitted intensity will be 50% the initial intensity. If this polarised light is then passed through a second filter, the transmitted intensity will obey Malus' Law.

This simulation by Geogebra allows us to visualise Malus law. By rotating the analyser we change the amplitude of the transmitted wave. The amplitude of the transmited wave is maximum at 0° or 180°, and zero at 90°.

## Video Lessons

 Chris Doner Polarisation IB Specific Gradepod Polarisation Question Examples IB Specific Khan Academy Polarisation of Light Physics Online Polarisation of Waves Practical Tips (Microwaves) Science Shorts Polarisation Basics Study Nova Polarisation & Malus' Law

## Resources

 IB Physics Topic 4 Notes IB-Physics.net Chapter 4 Summary IB Revision Notes Isaac Physics Polarisation Introduction Mr. G 4.3 Teaching Notes 4.3 Student Notes Physics and Maths Tutor Waves Definitions Waves Key Points Waves Detailed Notes Waves Progressive & Standing Waves A Level Resources - content slightly different

## Questions

 Cambridge University Press Topic 4: Add Qs Topic 4: Add Qs MS Topic 4: MCQs CUP Website Link Freely available online Dr French's Eclecticon Interference, Doppler, Polarisation Interference, Doppler, Polarisation Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 4.3 (Polarisation) MCQ Topic 4 (Waves B) End Quiz Quick IB Specific Mixed MCQs Isaac Physics Polarisation Mr. G 4.3 Formative Assessment Topic 4 Summary Qs IB Specific Questions Physics and Maths Tutor Waves (AQA 1) Waves MS (AQA 1) Waves (OCR) Waves MS (OCR) A-Level Qs: overlapping content Physics and Maths Tutor Waves (Edexcel 1) Waves MS (Edexcel 1) Waves (Edexcel 2) Waves MS (Edexcel 2) A-Level Qs: overlapping content