Waves

ELATE E-LEARNING AND TEACHER EDUCATION.

TEACHERS’ GUIDE

Subject: Physics

Unit: 4

Topic: Waves

Sub-topic: Characteristics of waves on ropes, springs and water.

Form: S.3

Introduction

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.

We make use of waves in every day life situation. e.g. Telephone communication, Radio communication, Beats in musical instruments etc.

Concept of waves:

• 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.

• Wave motion is due to a transfer of energy from one particle to the next particle 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.

ICT/ILLUSTRATOR REQUEST

1. Radio presenter in a studio
2. Musician playing a guitar.
3. Earthquake bringing down buildings.

Brief description of topic.

You 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

Time required: Minimum: 160 minutes, Maximum: 200 minutes

Learning objectives:

By the end of this topic, learners should be able to:

• Give examples of waves and state how they are formed.
• Carryout experiments to demonstrate wave formation and motion using strings /ropes, rubber tubing, slinky springs, ripple tanks e.t.c
• Explain wave and wave motion as means of transfer of energy from source of disturbance to another point in the medium without net transfer of matter of the medium through which the wave travels.
• Construct wave model.
• Explain how waves move from one point to another.
• Draw graphical representation of wave motion – displacement against distance and displacement against time.
• Define terms associated with waves motion.
• Derive the wave equation V=f λ.
• Distinguish between stationary and progressive waves, transverse and longitudinal waves.

Forms of wave fronts:

Wave front is a surface, which passes through all particles which are vibrating in PHASE in the path of a wave.

1. Circular wave fronts

Example: 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.

(b) Straight wave fronts.

Example: water ripples formed by dipping a rod horizontally into water.

Terminology used in wave motion

Considers several leaves lying in line on the surface of water.

When a disturbance is caused on the water a wave moves a long the line of the leaves causing each of the leaves to be displaced from the undisturbed /equilibrium position.

a = amplitude

amplitude is maximum displacement from equilibrium position. It is measured in metres.

ג = wavelength

Wave length is distance between two successive crests, it is also measured in metres.

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 in hertz (H_z) or cycles per second.

i.e. 1000 Hz = 1 k Hz and 1,000,000 Hz = 1 M Hz

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.

Time	Number of cycles
T	1	Definition of period
1	1/T	Definition of frequency

From the table above

f = 1/T

The wave formula

Now 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 therefore,

ג = v x 1/f

Hence, v = f ג

Description of wave motion (graphical representation)

Graphical representation of wave motion

There 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 WAVES

Transverse waves

Let us look at several leaves floating on water surface in line again. The relative movement of each of the leaves at a given time is shown in the diagram.

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 the 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 5^th edition) by A F. Abbot pg287-289.

1. 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.

2. 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.

3. 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.

Longitudinal waves

When 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 particle to the next one in the air and thus a compression effect (pulse or signal) moves forward.

When B moves to the left, a region of low density called the rarefaction (R) is created which also moves forward. Therefore as the prong vibrates, compressions and rarefactions move forward. This is called a 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 Waves

When two waves of the same frequency, wavelength and amplitude travelling in opposite directions meet, the resulting effect is a stationary wave. The diagram below shows a stationary wave.

In a stationary wave there exists points of zero displacement called nodes (N) and points of maximum displacement called antinodes (A).

Please 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.

Exercise.

1. (a) Define a wave.

(b) Distinguish between longitudinal and transverse waves giving examples of each.

(c) Define the following terms:

(i) Wavelength.

(ii) Period.

(iii) Frequency.

2. State the characteristics of a stationary wave.

3. (a) Show that the velocity of a wave, v = f

(b) An FM radio station broadcasts at frequency 88.8MHz. If velocity of electromagnetic waves is 3 x 10⁸ ms^-1, find wavelength and the period of the waves.

1. (a) A wave is a means of transfer of energy by a vibrating medium.

(b) a transverse wave is one where the direction of vibrations of the particles in the medium is perpendicular to the direction of wave motion. For While longitudinal waves are those where the vibrations of particles are parallel to the direction of wave motion.

Examples of transverse waves are water ripples and electromagnetic waves.

Examples of longitudinal waves are sound waves and ultrasonic waves.

(c) (i) wavelength is the distance between tow successive particles that are in phase.

(ii) period is the time taken to complete one cycle.

(iii) frequency is the number of complete cycle made per second.

2. The characteristics of stationary waves:

• Particles between nodes vibrate in phase.
• Each particle has its own amplitude.
• Points with maximum displacement are called antinodes.
• 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.

3. (a)

Note that:

• Distance AB = Wave velocity x Time taken to move from A to B.

ג = v x T

But , T = 1/f and therefore,

ג = v x 1/f

Hence, v = f ג

(b) v = f ג

3 x 10⁸ = 88.8 x 10⁶ x ג

ג = 3.38m

T = 1/f = 1/88.8 x 10⁶ = 1.13 x 10^-8 s