3.3 wave behaviour

Dr Pusey

www.puseyscience.com

Use wave-front and ray diagrams to describe wave behaviour

Describe the reflection of waves when incident upon a surface

Describe the refraction of waves as they move from one medium to anotherApply Snell’s Law

Describe diffraction and the effects of wavelength on the amount of diffraction that occurs.

Describe wave intensity and the inverse square lawApply the relationship

𝐼 ∝1

𝑟2

Wave Representation Wave propagation can be modelled as rays or wave

diagrams, depending on what you’re trying to display or do:

Wave Diagram or Wave-front Diagram

Depicts changes in wavelengthAlso good to show diffraction andspreading of waves

Ray Diagram

Useful to show change in wave direction (reflection and refraction)

Reflection We use rays to depict direction of reflection of waves

Angle of Incidence (relative to the NORMAL) is the same as the Angle of Reflection (relative to the NORMAL)

θrθi

θrθi

Normal (perpendicular to the surface) Normal (perpendicular to the surface)

wave-fronts

Reflection – Changes in Phase When a wave in reflected from a fixed (closed) end, it

undergoes a phase shift of half the wavelength (inverted) If a wave is reflected from an free (open) end, it will reflect

with no phase change.

This complex behaviour of waves is quite important for signal processing.

See for yourself:https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html

Keith Gibbs - www.schoolphysics.co.uk

Refraction of Waves Changes the direction of a wave

Occurs when a wave enters a medium and travels at a different speed.

Occurs at the BOUNDARY between the two media

Every Day Examples of Refraction: You can see the bottom of a glass easier if it is full of

water

You appear shorter when standing in a pool of water

Rainbows

DOUBLE RAINBOWS!

Diamonds glimmering (Total Internal Reflection)

Refraction of Waves

Heinemann 3A/3B, P195

Snell’s Law Describes how waves are

refracted

Works with mechanical and electromagnetic waves

𝑠𝑖𝑛𝜃𝑖𝑠𝑖𝑛𝜃𝑟

=𝑣1𝑣2

=𝜆1𝜆2

If velocity drops, so does wavelength and the angle of refraction

Draw what happens as the wave continues

Faster speed

Slower speed

Normal

Normal

Faster Speed

θi

θr

Snell’s Law Describes how waves are

refracted

Works with mechanical and electromagnetic waves

𝑠𝑖𝑛𝜃𝑖𝑠𝑖𝑛𝜃𝑟

=𝑣1𝑣2

=𝜆1𝜆2

If velocity drops, so does wavelength and the angle of refraction

Draw what happens as the wave continues

Faster speed

Slower speed

Faster Speed

θi

θr

θi

θr

Snell’s Law

Question – From Water to Air

𝑠𝑖𝑛𝜃𝑖

𝑠𝑖𝑛𝜃𝑟=

𝑣1

𝑣2

v1 = 2.25x108 m/s

v2 = 3.00x108 m/s

If the angle of incidence was 40.0°, what is the angle of refraction?

If the angle of incidence was 50.0°, what is the angle of refraction?

(Light in Water)

(Light in Air)

Question – From Water to Air

𝑠𝑖𝑛𝜃𝑖

𝑠𝑖𝑛𝜃𝑟=

𝑣1

𝑣2

v1 = 2.25x108 m/s

v2 = 3.00x108 m/s v1/v2 = 2.25/3 = 0.75

If the angle of incidence was 40.0°, what is the angle of

refraction? 𝑠𝑖𝑛𝜃𝑟 =𝑠𝑖𝑛40

0.75= 0.857 𝜃𝑟=59.0°

If the angle of incidence was 50.0°, what is the angle of

refraction? 𝑠𝑖𝑛𝜃𝑟 =𝑠𝑖𝑛50

0.75= 1.02 𝜃𝑟=??????

(Light in Water)

(Light in Air)

Total Internal Reflection When the angle of incidence

is larger than a certain angle, a wave will not be refracted. It will be reflected.

This critical angle is given

by the formula 𝑠𝑖𝑛𝜃𝑐 =𝑣1

𝑣2

This is the principle of light propagation within Fibre Optic cabling (fancy sound systems, NBN, etc)

Diffraction Diffraction is the spreading of waves following an obstacle

or as it pass through an opening/slit/aperture

The amount of diffraction that occurs depends on the relationship between the wavelength and the opening size.

Heinemann 3A/3B Page 198

Diffraction Diffraction explains why low frequency sounds are hard

locate and high frequency sounds are easy to locate.

Diffraction explains why you can hear low frequency music outside the door of a nightclub while high frequency sounds require you to be in-line with the speakers

Diffraction explains why Dr Pusey’s sub woofer is in the corner of his lounge room. Since the sub woofer only outputs low frequency sounds and these spread rapidly, our ears can’t really tell where it is. The best lounge-room spots are reserved for tweeters, with high frequency output where directionality is high.

photo credit: Fjellanger Widerøe A.S.; image source

Intensity Intensity is the amount of light/sound power per unit of

area. So it’s measured in Watts per Metres Squared –W/m2

.

You can see that as we move far from a source, the power spreads out over a greater area, reducing the power per square metre (intensity)

Inverse Square Law 𝐼 ∝1

𝑟2 If we assume spherical wave spreading (which we do), we

can say that waves obey the inverse square law:

As the wave propagates a distance, r, away from the source, the intensity of the wave decreases by r2. (more on next slide)

Inverse Square Law 𝐼 ∝1

𝑟2 Q: If the distance from a light source doubles, what

happens to the intensity?

A: the change in r is a factor of 2, then the change in I is a factor of (1/22) = 1/4. So the Intensity will be reduced by a factor of 4. 2𝑟1

Inverse Square Law 𝐼 ∝1

𝑟2 The ratio between the Intensity and 1/distance2 which

looks like this: 𝐼1

𝑟2

must always be constant for a given

source. So:

We can use ratios to find information about a second location using the following relationship:

𝐼11

𝑟12

=𝐼21

𝑟22

Rearranged: 𝑰𝟏

𝑰𝟐=

𝒓𝟐𝟐

𝒓𝟏𝟐 This is your friend!

Inverse Square Law 𝐼 ∝1

𝑟2 Knowing this relationship, we can determine the intensity,

I, at a distance r away from a source, if we know the intensity at any other location.

𝐼1𝐼2=𝑟2

2

𝑟12

E.G.

Three metres from a light source the intensity is 240 W/m2. What is the intensity at 1.5m?

Inverse Square Law 𝐼 ∝1

𝑟2 Knowing this relationship, we can determine the intensity,

I, at a distance r away from a source, if we know the intensity at any other location.

𝐼1𝐼2=𝑟2

2

𝑟12

E.G.

Three metres from a light source the intensity is 240 W/m2. What is the intensity at 1.5m?

240

𝐼2

=1.52

32

240×9

2.25= 𝐼2 =960 W/m2

Other things to do with waves Doppler effect – Movement can compress or expand the

distance between waves, changing the wavelength. This explains why car sirens sound different when they are coming towards you and going away from you. It’s also used a huge amount in astronomy.

Light dispersion – The amount of refraction also depends on the frequency. This is why different light colours refract at different amounts. When light is passed through a raindrop, the dispersion produces a rainbow.

Beats – Two frequencies at the same time can produce beats if the difference in those frequencies is below the audible range. The number of beats per second is the difference in frequencies! These can be heard in the cabin when a planes takes off: two engines with an ever-so-slight RPM difference.

Use wave-front and ray diagrams to describe wave behaviour

Describe the reflection of waves when incident upon a surface

Describe the refraction of waves as they move from one medium to another Apply Snell’s Law

Describe diffraction and the effects of wavelength on the amount of diffraction that occurs.

Describe wave intensity and the inverse square law Apply the relationship

𝐼 ∝1

𝑟2