# Physics Tutorial: Diffraction of Waves

In this Physics tutorial, you will learn:

• What is diffraction?
• What are the conditions for diffraction to occur?
• What happens to the shape of waves in diffraction?
• What is the relationship between diffraction and interference?
• What does Huygens Principle say on diffraction of waves?

## Introduction to Diffraction of Waves

What happens to water when you put a finger under the tap? Does water turn back on the tap or it continues falling down? Is the direction of water the same as before putting the finger under the tap? Why?

What happens to water waves when they encounter a stone during their path? Do they turn back or they continue moving on their way?

What occurs to the shape of waves when they pass through a narrow gap? Do waves have the same shape as before?

All these questions will get answer in this tutorial. Therefore, please read it before jumping to other tutorials as this tutorial sheds light to many questions which will arise during the study of waves. Also, the information provided in this tutorial will form the base for the next section.

## What is Diffraction?

By definition, diffraction is the process by which a wave is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the waveforms produced.

The condition to obtain diffraction is that the dimensions of aperture or of the obstacle must be comparable to wavelength. When the aperture is much larger than the wavelength, no diffraction occurs and when the aperture is smaller than wavelength, circular wavefronts are produced. To understand diffraction, you can use the analogy of entering through a narrow gate, in which you must change your position, i.e. turn by 900 to pass through the gate. But if the gate is wide, you pass through it without problem.

Look at the figure below in which diffraction of water waves in a ripple tank is shown. Initially, the wave in the figure was moving in one direction. After entering the narrow aperture, it spreads in all directions as the aperture here acts as a new wave source. As a result, the wave shape changes from straight to round.

If the aperture enlarges, waves straighten because they experience diffraction only at the edges of aperture, as shown in the figure below. The same phenomenon occurs when a wave encounters a small obstacle as well. Look at the figure. For example, diffraction of sound waves enables us to hear even when the speaker is round a corner of a building. This is because sound waves produced by the speaker bend around small obstacles such as the building walls.

Diffraction of sound waves is commonly observed in everyday life. For example, many forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound waves. Owls for instance are able to communicate across long distances due to the fact that their long-wavelength hoots are able to diffract around forest trees and carry farther than the short-wavelength tweets of songbirds.

The following two actions helps us understand the operation mode of diffraction.

1) When you hit a poplar trunk using a thin stick, the stick will bend around the trunk. 2) When you put your finger under the tap, water first passes around your finger and then, it falls on the sink. When a simultaneous diffraction occurs through two openings, an interference pattern is produced. Therefore, diffraction and interference are related concepts as interference is produced when diffraction from two or more openings does occur. In this way, we can say "diffraction from two or more sources produce interference but interference cannot produce diffraction." Therefore, the relationship between diffraction and interference is unilateral.

The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength for a constant opening. In fact, when the wavelength of the mechanical wave is smaller than the obstacle, no noticeable diffraction occurs.

Diffraction of water waves is observed in a harbor as waves bend around small boats and are found to disturb the water behind them. The same waves however are unable to diffract around larger boats since their wavelength is smaller than the boat.

### Example 1

A number of straight and parallel water waves are shown in the figure below. The distance between every two crests is 8 cm. After passing through two small gaps that are 40 cm away from each other, water diffracts and circular wavefronts are produced.

Calculate the time needed for the interference to produce if waves move at 2 cm/s.

### Solution 2

Waves move towards each other in the lateral part of the two gaps. Therefore, their relative speed is 2 cm/s + 2 cm/s = 4 m/s. Thus, it takes 40 cm / 4 m/s = 10 s for the interference to produce.

## Huygens Principle

The Dutch scientist Christiaan Huygens developed a useful technique for determining in detail how and where waves propagate during diffraction. Starting from some known position, Huygens's principle states that every point on a wave front is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wave front is tangent to all of the wavelets.

We saw the application of Huygens Principle in all examples discussed so far. For example, if a door is 73.5 cm wide and a 1400 Hz sound wave moving at 343 m/s passes through it, there are three simultaneous wavefronts produced, as

λ = v/f
= 343 m/s/1400 Hz
= 0.245 m
= 24.5 cm

Therefore, since the width of the door is d = 73.5 cm, the number of waves that can pass simultaneously through the door is

N = d/λ
= 73.5 cm/24.5 cm
= 3

Look at the figure below: We will discuss more extensively Huygens Principle and diffraction in general in our Physics tutorial on "Interference and Diffraction of Light", where more numerical examples and techniques will be explained.

## Physics Revision: Diffraction of Waves Summary

By definition, diffraction is the process by which a wave is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the waveforms produced.

The condition to obtain diffraction is that the dimensions of aperture or of the obstacle must be comparable to wavelength. When the aperture is much larger than the wavelength, no diffraction occurs and when the aperture is smaller than wavelength, circular wavefronts are produced. If the aperture enlarges, waves straighten because they experience diffraction only at the edges of aperture. The same phenomenon occurs when a wave encounters a small obstacle as well.

Diffraction of sound waves enables us to hear even when the speaker is round a corner of a building. This is because sound waves produced by the speaker bend around small obstacles such as the building walls.

Diffraction and interference are related concepts as interference is produced when diffraction from two or more openings does occur. Diffraction from two or more sources produce interference but interference cannot produce diffraction. Therefore, the relationship between diffraction and interference is unilateral.

The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength for a constant opening. In fact, when the wavelength of the mechanical wave is smaller than the obstacle, no noticeable diffraction occurs.

The Dutch scientist Christiaan Huygens developed a useful technique for determining in detail how and where waves propagate during diffraction. Starting from some known position, Huygens's principle states that every point on a wave front is a source of wavelets that spread out in the forward direction at the same speed as the wave itself. The new wave front is tangent to all of the wavelets.

## Physics Revision Questions for Diffraction of Waves

1. Straight parallel water waves of 80 cm distance from each other pass through four openings of different size. In which opening does not occur any noticeable diffraction?

1. 8 mm
2. 8 cm
3. 80 cm
4. 8 m

2. A number of straight and parallel water waves are shown in the figure below. The distance between every two crests is 6 cm. After passing through two small gaps that are 30 cm away from each other, water diffracts and circular wavefronts are produced.

Calculate the wave speed if the time needed for the interference to produce is 10 s.

1. 3 cm/s
2. 4 cm/s
3. 5 cm/s
4. 6 cm/s

3. How many simultaneous sound wavefronts of frequency equal to 800 Hz are produced when sound passes through a 85 cm wide door?

1. 0
2. 1
3. 2
4. 3