Nodal Line and Anti-nodal Line

1. An anti-node is a point of maximum amplitude where constructive interference occurs. Whereas a node is point of minimum amplitude where destructive interference occurs.
2. The anti-nodal line joins all anti-node points. The nodal line joins all node points.

Formula for Interference

The distance between two antinode line, x, can be related to the wavelength, λ, by the follwing equation:

λ = Wavelength
a = Distance between the two wave sources
x = Distance between two successive anti-node lines or node lines
D = Distance from the wave sources to the plane where x is measured.

 

The principle of superposition states that where two or more waves meet, the total displacement at any point is the vector sum of the displacements that each individual wave would cause at that point.

(Meeting of two peaks)

 

(Meeting of a peak and a trough)

Coherent Wave

Two wave sources which are coherent have same frequency or have constant phase difference.

 

1. The effect of superposition of two coherent waves is interference.
2. Interference is a phenomenon of wave caused by the superposition of 2 or more coherent waves.
3. The effect of interference can be studied using a ripple tank. Two dippers are used to produce two sources of coherent waves.
4. Figure 3 shows the interference pattern observed.
5. Interference can be constructive or destructive.

Constructive Interference and Anti-node

1. In the interference of 2 waves, there are places where the 2 waves are always in phase (same phase) and the superposition of the waves produces oscillation with maximum amplitude. This is called the constructive interference.
2. A place where constructive interference occurs is called the anti-node.

Destructive Interference and Node

1. In the interference of 2 waves, there are also places where the 2 waves are always anti-phase (phase difference = 180°) and the superposition of the waves produces oscillation with minimum amplitude. This is called the destructive interference.
2. A place where destructive interference occurs is called the node.

 

Experiment

 

Pin Hole Experiment

1. Light is diffracted when passes through a pin hole.
2. Diffraction pattern is made up of alternate bright and dark ring..

Single Slit Experiment

1. Light is diffracted if it passes through a narrow slit.
2. Diffraction pattern is made up of the bright bands and dark bands of different width.
3. The central band is wider and brighter. The dark and bright bands of narrower width are alternatively observed on the left and right side of the central bight band.
4. Diffraction pattern obtained will be clearer if the size of the slit decreases.
5. Conditions for diffraction to take place are:
   1. Light source must be monochromatic. That is, the light must possess only one wavelength.
   2. Slit size must be small enough as compare with the wavelength of light.

Factors affecting the pattern of diffraction

The factors that will affect the distance between the bright bands are

1. Size of the slit
2. Colour of the light
3. Distance of the screen from the slit

 

1. Diffraction is the spreading of a wave when it travels through an opening or a small obstacle.

(Diffraction happen when waves pass through an opening)



(Diffraction happen when waves encounter an obstacle)


2. Characteristics of Diffracted Wave
   1. Wavelength does not change.
   2. Frequency does not change.
   3. Speed of diffracted does not change.
   4. The amplitude of the wave decreases after diffraction.

Factors Affecting the Magnitude of Diffraction

The magnitude of diffraction (or angle of diffraction) depends on

1. The wavelength
2. The size of the opening

Experiment 1

Shorter wavelength - The wave spreads to a smaller area

Longer wavelength - The wave spreads to a wider area

Conclusion:
Diffraction is affected by the wavelength. The longer the wavelength, the greater the effect of diffraction

Experiment 2

Bigger opening - The wave spreads to a smaller area

Smaller opening - The wave spreads to a wider area

 

1. When light travels one medium to another of differing density, its speed changes.
2. Speed of light is higher in a medium of less density as compare with one higher density. The change in velocity of light when it travels from one media to another of different density results in the refraction phenomenon.
3. As we have learned in form 4 chapter 5, light, the refraction of light obey the law of refraction, where $$\frac{\sin i}{\sin r}=\text{constant}$$

 

 

Speed of Water Waves

1. When straight waves pass from deep to shallow water, their
   1. wave-length becomes shorter
   2. speed decreases
   3. frequency remain unchanged
2. This can be illustrated by placing a piece of rectangular Perspex of suitable thickness in the tank to reduce the local water depth.
   
3. Figure below shows the wavefront diagram of the wave formed.
   
4. We can see that the wavelength above the Perspex is shallower.
5. The relationship between the speed and wavelength of the wave in deep and shallow region is given by the formula below.
6. 
7. v_d = speed of wave in deep region
   λ_d = speed of wave in deep region
   
   
   v_s = speed of wave in deep region
   λ_s = speed of wave in deep region

Refraction of Waves at a Boundary

1. Refraction is the change in direction of propagation when a wave moves from one medium to another medium.
2. It is caused by the change of the speed of the wave when moving from one medium to another.
3. For water waves, refraction occurs when the waves move from one region to another region of different depth.
4. If water waves pass through a shallow region of convex shape, the waves will be converged.
   
5. If water waves pass through a shallow region of concave shape, the waves will be diverged.
   

 

Experiment

Conclusion:

1. The angle of incidence, i is equal to the angle of reflection, r.
2. Sound waves obey the law of reflection. That is, the angle of incidence is equal to the angle of reflection.