Diffraction of Waves

Diffraction is:

the spreading out of waves after they pass through a narrow gap or around an obstruction

- When waves meet a narrow gap they must curve to pass through
The extent of their diffraction depends on the width of the gap compared to the wavelength of the waves

$Diffraction Wavefronts, downloadable AS & A Level Physics revision notes$

Diffraction: after passing through a narrow gap, the waves curve as they spread out

The only property of a wave that changes when it diffracts is its amplitude
- The wavelength of the wave remains the same
The amplitude of the diffracted waves is less than that of the incident waves since energy is distributed over a larger area
Imagine trying to squeeze yourself through a narrow gap. How do you do it?
- You make yourself narrower
- A wavefront will do the same
The greater the wavelength of the wave, the greater its diffraction
Examples of diffraction include:
- Radio waves moving in between or around buildings
- Water waves moving through a gap into a harbour

As the gap size increases, compared to the wavelength, the amount of curvature on the waves gets less pronounced
- This is because the wave has to curve less to fit through the gap
When the gap is much larger than the wavelength then it no longer curves and no longer spreads out after passing through the gap

$Diffraction gap size, downloadable AS & A Level Physics revision notes$

The size of the gap (compared to the wavelength) affects how much the waves spread out when diffracted through a gap

Diffraction can also occur when waves curve around an edge
- The waves spread out to fill the gap behind the object
The extent of this diffraction also depends upon the wavelength of the waves
- The greater the wavelength then the greater the diffraction

$Diffraction on an edge, downloadable AS & A Level Physics revision notes$

When a wave goes past the edge of a barrier, the waves can curve around it

Worked example

An electric guitar student is practising in his room. He has not completely shut the door of his room, and there is a gap of about 10 cm between the door and the door frame.

Determine the frequencies of sound that are best diffracted through the gap.

The speed of sound can be taken to be 340 m s^–1

Answer:

Step 1: Optimal diffraction happens when the wavelength of the waves is comparable to (or larger than) the size of the gap

λ = 10 cm = 0.1 m

Step 2: Write down the wave equation

$v = f λ$

- where v = 340 m s^–1

Step 3: Rearrange the above equation for the frequency f

$f = \frac{v}{λ}$

Step 4: Substitute the numbers into the above equation

$f = \frac{340}{0.1} = 3400 Hz$

The frequencies of sound that are best diffracted through the gap are:

f ≤ 3400 Hz

Worked example

When a wave is travelling through the air, which scenario best demonstrates diffraction?

A. UV radiation through a gate post

B. Sound waves passing a diffraction grating

C. Radio waves passing between human hair

D. X-rays passing through atoms in a crystalline solid

Answer: D

Diffraction is most prominent when the wavelength is close to the aperture size

Consider option A:

UV waves have a wavelength between (4 × 10^–7) and (1 × 10^–8) m so would not be diffracted by a gate post
Radio waves, microwaves or sound waves would be more likely to be diffracted at this scale

Consider option B:

Sound waves have a wavelength of (1.72 × 10^–2) to 17 m so would not be diffracted by the diffraction grating
Infrared, light and ultraviolet waves would be more likely to be diffracted at this scale

Consider option C:

Radio waves have a wavelength of 0.1 to 10⁶ m so would not be diffracted by human hair
- Infrared, light and ultraviolet waves would be more likely to be diffracted at this scale

Consider option D:

X-rays have a wavelength of (1 × 10^–8) to (4 × 10^–13) m
- This is a suitable estimate for the size of the gap between atoms in a crystalline solid
- Hence X-rays could be diffracted by a crystalline solid
Therefore, the correct answer is D

Exam Tip

When drawing diffracted waves, take care to keep the wavelength (the distance between each wavefront) constant.

Diffraction of Waves (SL IB Physics)

Revision Note