Diffraction – Learn

The bending and spreading of waves as they pass through a gap or around obstacles is called diffraction. Diffraction is why you can still hear sound waves from a speaker in another room, or why a water wave will spread through marina that has a small gap to the ocean.

Diffraction and slit width

Diffraction is significant when the size of the opening or obstacle is similar to or smaller than the wavelength of the wave. We can express this mathematically by saying that significant diffraction occurs when \cfrac { \lambda }{ w } \ge 1. Where \lambda = wavelength and w = slit width.

When the slit width is much greater than the wavelength than diffraction only occurs at the edges.

The following diagram illustrates how diffraction occurs at a gap that is a) larger than the wavelength, and b) smaller than the wavelength:

Check out the following link to play with a variety of diffraction simulations:

Diffraction simulation

Example 1:

Describe the differences in diffraction that would occur in the following situations:

a) A 20cm wavelength and a 1m gap:

b) A 5cm wavelength and a 1cm gap:

c) A 2cm wavelength and a 1 cm gap:

Answers:

a) Minimal diffraction at the edges

b) Large degree of circular diffraction

c) Large degree of diffraction. Not as circular as b). (ratio in b = 5 and in c = 2)

Example 2:

A sound wave is passing through a door with a gap of 1.2m. What is the frequency of a wave that has the same width as the door opening?

\lambda =1.2m

speed of sound in air, c=340{ m }/{ s }

using; v=f\lambda , (c=f\lambda )  

340=f\times 1.2  

f=\cfrac { 340 }{ 1.2 }  

f=283.3Hz