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.

 

1. The characteristic of reflection of light enables us to see objects. Objects that do not emit light are not seen in the dark. An object only is seen if light is incident on it a reflected back to our eyes

Experiment

2. The experiment of reflection of light wave shows that reflection of light wave obeys the law of reflection.

 

1. Reflection occurs when an incident wave hits a reflector and reflected back.
2. The direction of propagation of the wave changed when it is reflected.
3. The wavelength, frequency and speed of wave remain unchanged.
4. The amplitude of the wave may or may not change depend on the material of the reflector and the shape of the wavefront.

Reflection of Straight and Circular Wave

1. Reflection of waves obeys the law of reflection, that is
   1. The angle of incident is equal to the angle of reflection
   2. The incident wave, reflected wave and the normal lie on the same plane.
2. For reflection of circular wave, the distance of image from the reflector is equal to the distance of source of wave from the reflector.

(Reflection of Straight Plane Wave)

(Reflection of Circular Wave)

 

Phenomena of Waves

1. There are 4 phenomena of waves:
   1. Reflection
   2. Refraction
   3. Diffraction
   4. Interference
2. Diffraction and interference are unique phenomena. Only waves perform these phenomena.
   
   

 

Natural Frequency

The Natural frequency of an oscillating system is the frequency of the system when there is no external force or forces acting on it.

Damping

1. Damping is the decrease of amplitude of an oscillating system.
2. An oscillating system experiences damping when its energy is losing to the surrounding as heat energy.
3. Usually, the frequency of the system remain unchanged.

(Displacement-time graph of a damped oscillation)

(Amplitude-time graph of a damped oscillation)

Type of Damping

Damping can be divided into:

1. internal damping, where an oscillating system loses energy due to the extension and compression of the molecules in the system.
2. external damping, where an oscillating system loses energy to overcome frictional force or air resistance that act on it.

Force Oscillation

1. In a damped oscillation, external force must be applied to the system to enable the oscillation to go on continuously.
2. Oscillation with the help of external force or forces is called a force oscillation.

Resonance

In a force oscillation, if the frequency of the external force is equal to the natural frequency of the system, the system will oscillates with maximum amplitude, and this is named as resonance.

Examples of Resonance

1. Opera singer breaks a wine glass with her voice due to the effect of resonance.
2. Tacoma Narrow Bridge in USA collapsed in 1940 due to the effect of resonance.
3. A moving bus produces excessive noise at certain speed when the frequency of the engine equal to the natural frequency of the bus.

Bartons Pendulum

The characteristic of resonance can be demonstrated with a Barton’s pendulum system.


Observation:
1. When pendulum X oscillates, the other pendulums are forced to oscillate.
2. Pendulum D will oscillates with the largest amplitude.

 

 

Oscillation

1. Waves are formed by a series of oscillation.
2. In order to understand waves, we must understand oscillation.

Technical Terms Related to Oscillation

1. An equilibrium position is a point where an oscillating object experiences zero resultant forces.
2. A complete oscillation occurs when the vibrating object:
   1. moves to and fro from its original position and
   2. moves in the same direction as its original motion.
      
      
      
      
      
      
3. Amplitude is the maximum amplitude of an object from its equilibrium position. The SI unit for amplitude is meter, m.
   
   
   
   
   
   
4. The greater the amplitude, the greater the mechanical energy possessed by the oscillating system.
5. Period is defined as the time required for one complete oscillation or vibration .
6. Frequency, f is the number of oscillation that take place in one second. The SI unit for frequency is Herz (Hz).
7. Frequency can be related to period by the following equation
   
   f = frequency
   T = Period
   
   

In a displacement-time graph, we can determine

1. The displacement of the oscillating object at any time.
2. The amplitude
3. The period.

Comparing Displacement-Time Graph and Displacement- Distance Graph

（Displacement-time graph - Graph of oscillation)

(Displacement-distance graph - Graph of Waves)

1. Both the displacement-time graph and the displacement distance graph looked similar. However they are 2 different types of graph.
2. The displacement-time graph illustrate the displacement of an object over time whereas the displacement-distance graph tell the position of the vibrating particles of a wave.
3. For a displacement- distance graph, the distance between 2 crest/trough represent the period whereas for the displacement-distance graph, it represents the wavelength.

 

1. A Displacement – Distance graph shows the position of each particle in a wave relative to its distance from a reference point.
2. The distance between two (2) successive crest or trough is the wavelength.
3. The maximum displacement of the particles from the equilibrium position (displacement = 0) is the amplitude.
4. The amplitude of the wave will increase as the energy transfers by the wave increase and vice versa.

 

Waves can be classified into 2 groups

1. transverse wave
2. longitudinal wave
   

Transverse Wave

Longitudinal Wave

Transverse Wave – Crest and Trough

1. When discussing wave, it’s important to know what is meant by the crest and trough of a wave.
2. The point at which the displacement of the water from its normal level is highest called the crest of the wave
3. The point at which the displacement of the water from its normal level is lowest called the trough of the wave. 

Longitudinal Wave – Compression and Rarefaction

1. Unlike transverse wave, longitudinal waves have no crest and trough, instead, they have compression and rarefaction.
2. In compression regions of longitudinal waves, wave particles of the medium are packed closer.
3. In rarefaction regions, wave particles of the medium are packed further apart.

Finding Wavelength from a Diagram

Transverse Wave

Wavelength is the distance between two successive crest or trough.

Longitudinal Wave

Wavelength is the distance between two successive compression or rarefaction.

Wave front diagram

Wavelength is the distance between two successive wave front