# WAVES.

Specific objectives.

• Define a wave.
• Classification of waves.
• Describe the formation of pulses and waves.
• Describe transverse and longitudinal waves.
• Define amplitude, wavelength, frequency and velocity of a wave.
• Define the wave equation.
• Define the problem facing wave equation.
• Define the problem facing wave equation.
• Describe experiment to illustrate property of waves.
• Sketch wavefront to illustrate the property of waves.
• Describe experiment to illustrate stationary waves.
• Explain constructive and destructive interface.

Wave.

• A wave is a disturbance that moves away from the source carrying energy through a medium/vacuum. The particles oscillate or vibrate.
1. Oscillation- This is when a body moves to and from about a fixed point.
2. Vibration- When a portion of a body moves to and from relative to its fixed point.

Classification of waves.

• Waves can be classified into 3 categories.
1. The mode of propagation/transmission. This is whether they require a medium or not. There are two types.
2. Elastic waves/mechanical waves.
• These are waves that require a material medium for transmission.
• They are caused by a disturbance in a material medium e.g. water waves, sound waves, a wave in a stretched/spiral spring, earthquake.
1. Electromagnetic waves.
• These are waves that do not require a material medium for their transmission.
• They are caused by electromagnetic materials which are at right angles to each other and to the direction of the wave e.g. light, radio waves, x- rays, gamma rays, ultra violet, micro waves, infra waves.

1. The nature of propagation or transmission. This is whether the wave travel or is stationary. There are two types.
2. Progressive waves.
• These are waves that are travelling through a medium or vacuum.
1. Stationary waves.
• These are standing waves, they appear and disappear at the same time.

1. The nature of vibration of particles relative to the direction of travel of the wave. There are two types.
2. Transverse waves.
• These are waves in which the vibration of the particles is parallel to the direction of the wave e.g. water waves, electromagnetic waves, stretched string.
1. Longitudinal waves.
• These are waves in which the vibration of the particles is parallel to the direction of travel of the wave e.g. waves in a spiral spring.

Pulses.

• A pulse is a burst of wave energy caused by a disturbance on a medium.
• It can also be produced by disturbance in a room, string, spiral spring or dipping a finger on a straight edge on the surface of the water.

Characteristics of waves.

• All waves carry energy away from the source and repeat their motion.
• They all have one amplitude, wave length, frequency and velocity and periodic time.
1. Amplitude.
• This is the maximum displacement of a particle in wave motion.
• It is measured in meters.

2.Wavelength ( )

• Is the distance between any two consecutive particles that are at the same point in their path and are moving in the same direction.
• Is the distance between two consecutive crests or trough.
• Is the length of one wave or one vibration or one cycle.

3. Frequency.

• Is the number of complete oscillations made in a unit time.
• Is the number of complete cycles in a unit time.
• Is measured in Hertz (Hz) but has other units such as Megahertz MHz- 1,000,000 Hz and Kilohertz- 1,000 Hz.
1. Periodic time.
• It is the time to complete one cycle/ oscillations/wave.
• Is the time to cover one wavelength.
• It is measured in seconds (S).

Periodic time= Time/number of oscillations

T= 1/frequency

Velocity.

• It is the rate of change of displacement of a wave.

V= displacement/time      V= 1/T but 1/T is wavelength so V= Wavelength/time    V= frequency x wavelength

Waveform, wavefront and wavelet.

1. Waveform.
• Is the shape of a wave or pattern representing the vibration.
• It can be illustrated by drawing a graph of the periodically varied quantity against distance for one complete wavelength.

2. Wavefront.

• It is a line or surface within a two or three dimensional medium through which waves are passing being the locus of adjustment point at which the disturbances are in space.

Phase.

• As a stage that a periodic motion has reached, usually by comparison with another such motion of the same frequency.

In phase.

• When 2 varied waves have their maximum and minimum values occur at the same instance or particles in a wave motion which happen to be oscillated in the same level of displacement in their oscillation are said to be in phase.

Phase and phase difference.

• Waves can be of the same amplitude but different frequency and different amplitude.
• Particles in a wave motion which oscillates in the same direction under the same level of displacement in their oscillations are said to be in phase. They can be in phase even though they differ in amplitude.

Out of phase.

• Particles can be out of phase when they are always on opposite levels of displacement in their oscillations and moving in opposite directions.

Stationary waves.

• They are formed when two equal progressive waves travelling in opposite directions are superposed to each other.
• The two waves interfere to form points of no displacement called nodes. The form of such interference is referred to as destructive interference.
• The two waves cancel the effect of one another. They may interfere to form points of maximum displacement called antinodes. This interference is called constructive interference.

Nodes.

• They are points of no displacement.
• They are formed when a crest of one wave meet a trough of the second wave.
• They cancel each others motion and there is no displacement.

Antinode.

• They are points of maximum displacement.
• They are formed when a crest meet a crest or a trough meet a trough of the second wave.

Condition for formation of stationary waves.

• There must be two waves (They are called coherent waves).
• The two waves must be travelling in opposite directions and must have the same frequency, same wavelength, same amplitude and the same speed.

Properties of stationary waves.

1. It has nodes ant antinodes.
2. The vibration of particles at points between successful nodes is in phase but out of phase belong to the next segment.
3. Between successful nodes, particles have different amplitude of vibration.
4. They do not transfer energy away from the source.
5. The distance between two successful nodes or antinodes is a half wavelength and distance between a node and an antinode is a quarter wavelength.
6. It is produced by a superstition of two waves travelling in opposite directions.

Difference between progressive and stationary waves.

 Stationary waves Progressive waves The wave form do not move through the medium and therefore energy is not transferred away from the medium. The waves move through the medium away from the source hence carry energy away from the source. The distance between two successive nodes is ½ wavelength. The distance between two successive crests or troughs is equal to one wavelength. Vibration of particles between a point between successive nodes are in phase. Phase of particles near each other are different. The amplitude of particles between successive nodes are different. The amplitude of any two particles which are in phase is the same.

Properties of waves.

1. The bouncing of a wave from a reflecting surface.
2. The bending of a wave as it travels or cross from one medium to another of different density or depth.
3. The spreading of a wave round an opening or an obstacle.
4. Occurs when two waves of the same amplitude, wavelength and frequency are in phase travelling in the same direction and they meet.
5. Is a property of a wave where one plane of vibration is cut or blocked while the other plane is allowed to pass or received.