class 38 Properties of waves - Mr. Gopie...

PHYSICS WAVES

Mr Rishi Gopie

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Properties of waves

a) Reflection (at a plane boundary) – after which f, λ and speed (v) remain the same. consider:

i) Plane wavefronts

Diag. 9

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ii) Circular wavefronts

Diag. 10

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b) Refraction (at a plane boundary)

Diag. 11

Note the following:

i) λ1 > λ2

ii) f remains constant

iii) v1 > v2

iv) n = λ1/λ2 = v1/ v2 = sin i/ sin r

v) for water waves

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diag. 12

vi) Generally, for any type of wave (such as water waves, light waves, sound waves etc.):

1) wavelength is greater in the less dense medium

2) speed is greater in the less dense medium

3) frequency remains the same

4) refraction occurs towards the normal in the denser medium and away from the

normal in the less dense medium

5) for the denser medium:

n = wavelength (speed) of the waves in the less dense medium/wavelength (speed)

of the waves in the denser medium

6) Refraction occurs when a wave passes from one medium into another in which it

has a different speed and wavelength and the angle of incidence at the boundary

between the media is not zero.

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c) Diffraction

This is the spreading of waves as they pass through an opening or aperture such as a gap or

a slit (and as they pass around the edge of an obstacle) the width a. Of which is comparable

with the wavelength (λ) of the waves.

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Diag. 13

In all cases, for the emerging waves: f, λ and speed (v) remain the same as for the incident rays.

For a given width of opening/aperture/gap/slit (i.e. for a fixed a): increasing λ of the incident waves

increases the amount of diffraction, i.e. spreading of the waves (e.g. red light is diffracted more than

blue light , by the same opening, since λa > λb )

For a given wavelength of incident waves (i.e. a fixed λ): decreasing a increases the amount of

diffraction waves.

Since the wavelength of visible light are very small then the diffraction of light in ordinary

circumstances is not observed – instead, light appears to travel in straight lines rather than to be

diffracted. However, the wavelengths of the sound waves and water waves are usually much larger

than those for visible light and so their diffraction effects are much more common and easier to

observe – for instance, sound can be heard round obstacles, such as doorways, while the source of

the sound cannot be seen around the same obstacles. Also, water waves are observed to spread

through/around openings in ripple tanks (and in bays on coastlines).

June 2000 p2 q2

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d) Interference

The principle of superposition states that when two(or more) waves meet at the same point

in space the resultant displacement at that point is the vector sum of the individual

displacements that each of the waves would produce, by itself, at that point in space.

Coherent sources of waves are sources which produce waves that have a constant phase

difference between them. Such waves are said to be, themselves, coherent. They also have

the same wavelength, frequency and speed.

Interference between waves is produced where two (or more) coherent waves meet. The

waves undergo superposition and produce a pattern of resultant waves. This effect is

known as interference. Where the waves meet and undergo superposition in phase (i.e. with

crest – on – crest and trough – on – trough) then constructive interference occurs and the

amplitude of the resultant wave is the sum of the amplitudes of the two interfering waves. A

maximum of intensity is thus obtained.

Where waves meet and undergo superposition exactly out-‐of-‐phase, i.e. 180° out-‐of-‐phase

or in antiphase (with crest-‐on-‐trough and trough-‐on-‐crest) then destructive interference

occurs and the amplitude of the resultant wave is the difference between the amplitudes of

the two interfering waves. A minimum of intensity is thus obtained

Consider the following:

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Diag. 14

In a case of such interference the resultant wave (if there is one) has the same λ, f and speed

(v) as the interfering coherent wave.

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Consider the physical meaning of interference for various waves:

Examples of Waves Effects Produced for:

Constructive Interference Destructive Interference

Water Waves High Crests and lower troughs Lower crests and higher

troughs (or a flat surface for

interfering coherent waves of

the same amplitude)

Light Waves Brighter Light Dimmer light (or darkness for


the same amplitude.

Sound Waves Louder Sounds Softer sound (or silence from


the same amplitude.

All waves (and only waves – not particles ) can undergo diffraction and interference where

waves from 2 (two) coherent sources overlap, interference patterns are produced in the

region of overlap.

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Diag. 15

It is impossible to obtain two independent sources of light waves that are coherent, so a

single source must be divided into two secondary sources (such as a pair of slits i.e. double

slit). Since these two secondary sources come from the same primary source then the waves

they produce must be coherent. Young`s double slit experiment investigates an interference

pattern for light waves. Consider a typical arrangement.

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Diag. 16

The interference pattern is produced on a screen as a fringe pattern, i.e. a series of

alternating bright (B) and dark (D) fringes or bands. The centre of a bright fringe

corresponds to a region of constructive interference and the centre of a dark fringe

corresponds to a region of destructive interference.

The equation that applies in this situation is : 𝑥 = 𝜆𝐷/𝑑

Where x is the fringe separation (i.e. the distance between the centres of adjacent bright

fringes/bands).

D is the distance between the double slit arrangement and the screen, d is the slit separation

(i.e. the distance between the centres of the two slits), λ is the wavelength of the wave.

Once d and D are constant then𝑥 ∝ 𝜆, i.e. the fringes get closer together as the wavelength

of light decreases (for instance as the colour of the light changes from red to blue).

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Also, once λ and D are constant then 𝑥 ∝ 1/𝑑 , i.e. the fringes get closer together (for a

given colour, say) as the slit separation increases. The young double-‐slit experiment i)

demonstrates the wave nature of light (since only waves can undergo diffraction and

interference), ii) enables the value for the wavelength to be determined (by measuring , x, d,

and D and using the equation 𝜆 = (𝑥 ×𝑑) /𝐷

Since it is much easier to obtain a pair of coherent sources of sound waves then an

analogues experiment can be performed for sound waves. The primary source of light can

be replaced by an A.F. (audio frequency) generator and the double slit arrangement can be

replaced by a pair of identical speakers connected to the A.F. generator. In place of the

screen, a detector of sound waves is used – such as an observer`s ear of a microphone

connected to a cathode ray oscilloscope (c.r.o) or to a speaker.

Coherent water waves can be produced in a ripple tank (using dippers or barriers with gaps

in them) and an interference pattern obtained and observed. In fact, ripple tank

experiments can demonstrate all the properties of reflection, refraction, diffraction and

interference. Also all waves undergo superposition. In fact, only waves are capable of

undergoing superposition. In fact, only waves are capable of undergoing superposition

effects such as diffraction and interference – particles cannot show these properties.

class 38 Properties of waves - Mr. Gopie...

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