Chapter 1: Waves 1.1Understanding Waves. Motion of Waves 1 An oscillating or vibrating motion in which a point or body moves back and forth along a line

Chapter 1: Waves

1.1 Understanding Waves

Motion of Waves

• 1 An oscillating or vibrating motion in which a point or body moves back and forth along a line about a fixed central point produces waves.

Motion of Waves

• 2. Examples of waves:• (a) Light waves are produced as a

result of vibrations of electrons in an atom.

Motion of Waves

• 2. Examples of waves:• (b)Sound waves are produced by

vibrating mechanical bodies such as guitar strings or a tuning fork.

Motion of Waves

• 2. Examples of waves:• (c) Water waves are produced by

disturbance (or vibration) on a still water surface.

Propagation (Traveling) of Waves

• 1.When a wave travels through a medium, the particles of the medium vibrate about their equilibrium positions.

Direction of waves


• 2.However, the particles of the medium do not travel in the direction of the wave.


• 3 A wave transfers energy and the momentum from the source of the wave (the oscillating or vibrating system) to the surroundings.


• Activity 1.1: To demonstrate that waves transfer energy without transferring matter

• Apparatus:• Radio, candle and matches.


• Activity 1.1: To demonstrate that waves transfer energy without transferring matter

• Procedure• 1. A candle is placed about 10 cm from

the speaker of a radio.


• Procedure• 2. The candle is lit and the movements of

its flame is observed.


• Procedure• 3. Then, the radio is turned on and the

volume of the sound is gradually increased until a change in the movement of the flame becomes noticeable.


• Discussion• 1. The flame vibrates when the radio is

turned on.


• Discussion• 2. This observation shows that the

propagation of the sound waves from the vibration of the cone of the speaker transfers energy (or momentum) to the flame and causes it to vibrate.


• Conclusion• Waves transfer energy from a

vibrating system without transferring matter.

Wavefronts

• 1. A wave front is a line or plane on which the vibrations of every points on it are in phase and are at the same distance from the source of the wave.

Same

Phase

Wavefronts

• 2 . Points in a wave are in phase if they vibrate in the same direction with the same displacement.

Same

displacement

Plane Wave fronts

• 1 . Figure 1.3 shows the production of plane water waves when a wooden bar vibrates vertically at a constant frequency on the surface of the water.

Plane Wave fronts

• 2. Lines PQ, RS, TU and VW are straight lines along the respective crests of the waves. These lines are called wave fronts.

Circular Wave fronts

• 1. When we use a fingertip to touch the surface of water repeatedly, circular wave fronts are produced as shown in Figure 1.4.

Types of Waves

• There are two types of waves.• (a) Transverse wave • (b) Longitudinal wave

Transverse Waves

• 1. A transverse wave is a wave in which the vibration of particles in the medium is at right angle (perpendicular) to the direction of propagation of the wave.

Transverse Waves

• 2. A model of a transverse wave can be produced by a slinky spring as shown in Figure 1.6.

Transverse Waves

• 3. Examples of transverse waves are water waves and light waves.

Longitudinal Waves

• 1. A longitudinal wave is a wave in which the vibration of particles in the medium is parallel to the direction of propagation of the wave.

Longitudinal Waves

• 2. When the slinky spring is vibrated back and forth along the direction of propagation of the wave at a fixed rate, a longitudinal wave is produced as shown in Figure 1.8.

Longitudinal Waves

• 3 . Example of longitudinal waves is sound waves.

Amplitude, Period and Frequency of a Wave

• 1 . The amplitude, A, of a vibrating system is maximum displacement from its equilibrium position. It is a measure of height of the wave crest or depth of the wave trough.

Amplitude


• 2 . In Figures 1.9 (a) and (b), the distance OQ is the amplitude, where O is the equilibrium position of the vibrating system.

Amplitude


• 3 . The period, T, of a vibrating system is the time taken to complete an oscillation.

Period


• 4. In the two vibrating (oscillating) systems show in Figure 1.9, a complete oscillation are:

• (a) from P Q P or Q P Q, • (b) from OPQO or

OQPO


• 5. If a vibrating system makes n complete oscillations in a time of t seconds, the period of oscillation, T of the system is second

• The SI unit of period is second.

n

t


• 6 The frequency, f, is the number of complete oscillations made by a vibrating system in one second.

• The unit of frequency is hertz (Hz) or s-1.


• 7 From the formulae of T and f, the relationship between period, T and frequency, f is:

• T is inversely proportional to f and vice versa.


• Example 1:• In an experiment, Aziz observes that a simple

pendulum completes 30 oscillations in 48.0 seconds. What is

• (a) the period of oscillation?• (b) the frequency of oscillation?


• Example 1:• Solution• (a)

s6.130

48.0

oscllation completed ofnumber

takentimeTperiod,


• Example 1:• Solution• (b)

Hz625.06.1

1

T

1ffrequency,

Displacement-time Graph of a Wave

• 1. The sinusoidal graph in Figure 1.10 is a graph of displacement, s against time, t of a load on a spring.


• 2 From the graph of s against t in Figure 1.10, the following information is obtained.

• (a) Amplitude, A = a cm• (b) Period of oscillation, T is the time between

points:• (i) O and F, (ii) C and G or (iii) P and Q.


• Example 2:• Figure 1.11 shows the displacement-time graph

of the oscillation of a mass on a spring.

• Figure 1.11


• Example 2:• From the graph,• (a) state the amplitude,• (b) calculate the period of the oscillation,• (c) calculate the frequency of the oscillation.


• Example 2:• Solution• (a) Amplitude, A = 5 cm•

• Example 2:• Solution• (b) Period of oscillation, T =

0.04 s

• Example 2:• Solution• (c) Frequency of oscillation,

HzT

f 2504.0

11

Displacement-distance Graph of a Wave

• 1. Figures 1.12 (a) and (b) show the propagation of a water wave and a sound wave.


R: Rarefaction

C:Compression


• 2. The displacement, s of each particle of the medium at different distances can be shown in a displacement-distance graph as shown in Figure 1.12 (c).


• 3. The wavelength, , is the distance between successive points of the same phase in a wave.


• For example:• (a) the distance between two successive crests

or two successive troughs in a water wave,


• (b) the distance between two successive compressions or two successive rarefactions in a sound wave.The SI unit of wavelength, , is metre (m).


• Example 3:• Figure 1.13 shows a displacement-

distance graph of a wave.• Figure 1.13

• Find• (a) the amplitude,• (b) the wavelength of the wave.


• Example 3:• Solution• (a) Amplitude, A = 4 cm •


• Example 3:• Solution

• (b) Wavelength, =12 cm

Relationship between Speed (v), wavelength, and Frequency (f)

• The relationship between speed, wavelength and frequency can be obtained by relating the SI unit of the quantities.

fv


• Example 4:• A wave of frequency 120 Hz has a

wavelength of 5.0 m. What is the speed of the wave?


• Example 4:• A wave of frequency 120 Hz has a

wavelength of 5.0 m. What is the speed of the wave?

Solutionf = 120 Hz and =5.0mSpeed of wave, v = f = 120 x 5= 600 m s-1


• Example 5:• The displacement-distance graph in

Figure 1.14 shows the motion of a transverse wave. The source of the wave produces 10 complete waves in one second.

• Figure 1.14


• Example 5:• Calculate• (a) the amplitude,• (b) the wavelength, and • (c) the speed of the wave.

Relationship between Speed (v), wavelength, and Frequency (f)• Example 5:• Solution• (a) Amplitude, A = 6 cm•

Relationship between Speed (v), wavelength, and Frequency (f)• Example 5:• Solution• (b) Wavelength, = 20 cm•••

1o 2o

Relationship between Speed (v), wavelength, and Frequency (f)• Example 5:• Solution• (c) Frequency, f = 10 Hz, =

20 cm• Speed, v = f

=10x20

• = 200 cm s-1

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Chapter 1: Waves 1.1Understanding Waves. Motion of Waves 1 An oscillating or vibrating motion in which a point or body moves back and forth along a line