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Waves, waves, waves!!! Waves are everywhere .We are always bombarded by waves, seen or unseen. Here are some examples of waves: sound waves, visible light waves, radio waves, water waves, earthquake waves, waves on strings, waves on slinky springs, waves in flutes (pipe instruments). There are other phenomena the resemble waves e.g. motion of a pendulum of a clock, motion of mass hang on spring.
- Waves are formed by disturbances of particles in a medium. For example: Water ripples are formed by dipping a finger in a basin full of water.
- Sound waves are produced by a vibrating string.
- Waves are produced on a vibrating slinky spring by vibrating it.
- Wave motion is due to a transfer of energy from one particle to another in a medium. i.e. during wave motion a particle in a medium exerts a dragging force to its neighbouring particles.
- The direction of wave motion or the direction of energy transfer is called the ray. It is represented by a straight line with an arrow →.
We make use of waves in every day life situation. e.g. Telephone communication, Radio communication, Beats in musical instruments etc.How are waves involved in the following situations?
- Radio presenter in a studio
- Musician playing a guitar.
- Earthquake bringing down buildings.
Brief descriptionYou may be familiar with motion of cars, aeroplane, and human being walking or running where the object has net movement. In this topic you will learn about waves and wave motion where the object or medium has no net movement.Main content and concepts to emphasize
- Examples of wave motion in our environment.
- Experimental demonstration of wave motion on strings, slinky springs, ripple tanks, and rubber tubing.
- Concept, definition and explanation of wave motion.
- Description of wave and wave motion and definition of associated terms e.g. amplitude, frequency, period, velocity, wavelength, wave front, and phase.
- Graphical representation of wave motion.
- Establishment of the wave equation V=f λ
- Progressive and stationary waves.
- Transverse and longitudinal waves
Description of wave motion (graphical representation)Graphical representation of wave motionThere are two types of graphical representation of wave motion.(a) Displacement against distance for particles oscillating at single instant in time.(b) Displacement against time for single particle oscillating at a particular location.- The + and – on the displacement axis are only to show direction as displacement is a vector.- The smallest displacement occurs at zero (o) displacement.
TYPES OF WAVESTransverse wavesLet us look at several leaves floating on water surface in a straight line again. The relative movement of each of the leaves at a given time is shown in the diagram below.Note that :
- Leaf. A has attained maximum displacement and is about to start going down .
- Leaves B, C and D are still going up. Each of them will finally attain its maximum displacement and then move downwards to complete the cycle.
- Leaf E is at the lowest displacement and it is about to start going upwards.
- Leaves F, G, and H are still going downward and so on.
- Therefore, particles (i.e. leaves) of the medium move up and down as the wave moves on. This type of wave is called a transverse wave.
A transverse wave is one which causes particles in the medium to oscillate perpendicular to the direction of the wave motion.Examples of transverse waves: Water ripples, electromagnetic waves.Construction of a transverse wave model. (Adapted from physics 5th edition) by A F. Abbot pg287-289.
- On a plane piece of paper mark out and shade a series of stripes 2.5 mm apart and fold on the dotted series as shown on the diagram 1 below.
- Draw a wave curve as shown in diagram 2 below and shade the region between the curves. Cut out the shaded portion to form the wave strip.
- Insert the wave strip in the wave guide and move it along as shown in diagram 3, this will show you how the forward motion of wave is associated with vertical motion of wave particles.
- In a stationary wave there exists points of zero displacement called nodes (N) and points of maximum displacement called antinodes (A).Note:
- Particles between nodes vibrate in phase (the dotted lines show displacement of individual particles changing with time).
- Each particle has its own amplitude.
- Points with maximum displacement are called antinodes (A)
- The distance between two successive nodes is half a wavelength.
- The antinodes and the nodes don’t move along the medium.
- There is no net energy transfer in the direction of the waves.
- Such waves can be formed in pipes and on stretched strings.
[b]FORMS OF WAVE FRONTS[/b]Wave front is a surface, which passes through all particles which are vibrating in a PHASEin the path of a wave. There two forms of wave fronts namely: circular wave fronts or straight wave fronts.Circular wave frontsExample: Water ripples made by throwing a stone in a pool of water.Note: From the pattern above, the wave fronts are perpendicular to the rays.Straight wave frontsExample: water ripples formed by dipping a rod horizontally into water. Terminology used in wave motionconsiders several leaves lying in line on the surface of water.When a disturbance is caused on the water, a wave moves along the line of the leaves causing each of the leaves to be displaced from the undisturbed /equilibrium position as shown in figure below.[font=verdana,arial,helvetica,sans-serif]a = amplitude[/font][font=verdana,arial,helvetica,sans-serif]amplitude is maximum displacement from equilibrium position. It is measured in metres.[/font][font=verdana,arial,helvetica,sans-serif]ג = wavelength[/font][font=verdana,arial,helvetica,sans-serif]Wave length is distance between two successive crests, it is also measured in metres.[/font]Note the following:Each of the leaves attains the same maximum displacement as the wave passes it. The peak is seen to be moving away from the source in the direction of the wave. This type of wave is called a progressive wave.Some examples of progressive waves include: water ripples and sound waves in the air.If we now consider the behaviour of only one leaf floating on water with time as the wave passes it. The displacement of the floating leaf from the equilibrium/undisturbed position continuously changes with time as in diagram below.Note that:
- AB is a complete cycle or oscillation.
- Period (T) is the time taken to complete one full cycle and it is measured in seconds.
- Frequency(f) is the number of cycles made in one second and it is measured inhertz (Hz) or cycles per second.i.e. 1000 Hz = 1 k Hz and 1,000,000 Hz = 1 M Hz
- ∴ ג = v x 1/f Hence,v = f ג
Relationship between frequency and period.The relationship is easily obtained using the definitions of both period and frequency as can be seen from the following table.
[tr][td]Time[/td][td]Number of cycles[/td][td] [/td][/tr][tr][td]T[/td][td]1[/td][td]Definition of period[/td][/tr][tr][td]1[/td][td]1÷T[/td][td]Definition of frequency[/td][/tr]∴ From the table above f = 1÷TThe wave formulaNow let us look at the behaviour of several leaves floating on undisturbed water surface in a straight line. When a water wave passes these leaves, they will be displaced as shown in the diagram below.Note that: Distance AB = Wave velocity x Time taken to move from A to B. ג = v x T But , T = 1/f and Longitudinal wavesWhen the tuning fork is banged on a table its prongs vibrate and produce sound waves. When for example prong B goes to the right it compresses the air there and creates a region of high density called the compression C. This compression effect is passed on from one air particle to the next one and thus a compression effect (pulse or signal) moves forward.When B moves to the left, a region of low density called the rarefaction ® is created which also moves forward. Therefore as the prong vibrates, compressions and rarefactions move forward. This is called longitudinal wave.A longitudinal wave is one in which the particles of the medium vibrate parallel to the direction of the wave motion. Examples of longitudinal waves include sound waves and ultrasonic waves.Stationary WavesWhen two waves of the same frequency, wavelength and amplitude are travelling in opposite directions meet, the resulting effect is a stationary wave. The diagram below shows a stationary wave.