Chapter 12Physics Insights

WavesWaves

Learning OutcomeCandidates should be able to:

(a) describe what is meant by wave motion as illustrated byvibrations in ropes and springs and by waves in a ripple tank

(b) define speed, frequency, wavelength, period and amplitude

(c) state what is meant by the term wavefront

(d) show understanding that waves transfer energy withouttransferring matter

(e) recall the relationship velocity = frequency x wavelength

(f) apply the relationship between velocity, frequency andwavelength to new situations or to solve related problems

(g) *compare transverse and longitudinal waves and give suitableexamples of each

Examples of Waves

• Water Waves• Light & Sound Waves• Radio Waves (Carrying Electrical Signals)• Infra-Red Radiation (Transmitting data, taking

photos in the dark or through haze or fog)• X-rays (producing images for medical & industrial

purposes)• Ultra-violet Radiation (to start chemical reactions)

Introducing Waves

• Waves carry energy.– For Example, during an earthquake, the seismic waves

produced can cause great damage to buildings and thesurroundings.

• What is a wave?– A spreading of disturbance from one place to another.

For example, when we drop a pebble into a pond of stillwater, a few circular ripples move outwards, on thesurface of the water. As these circular ripples spreadout, energy is being carried with them.

Pictures by courtesy of Physics ClassroomPhotos by courtesy of Arttoday

Sources of Waves

• The source of any wave is a vibrationvibration oroscillationoscillation. For example, the forming of theslinky waves as shown.

• Wave motion provides amechanism for thetransfer of energytransfer of energy fromone point to anotherwithoutwithout the physicaltransfer of the mediumbetween the two points

Two Types of Waves

• Transverse WaveRope waves, Water waves,Light waves, Radio waves,Electromagnetic waves,“KallangKallang” waves.

• Longitudinal WaveSound waves and wavesproduced in a verticaloscillating spring under tension

Transverse Waves• Transverse waves travel

in a directionperpendicularperpendicular to thedirection of vibration

Longitudinal Waves• Longitudinal waves

travel in a directionparallelparallel to the directionof vibration

compressions

rarefactions

Waves AnimationTransverse Wave

Longitudinal Wave

Website :http://www.gmi.edu/~drussell/Demos/waves/wavemotion.html

Wave Applets

Surface Waves

Describing Waves•• Crests and troughsCrests and troughs

– High points and low points that characterise transverse waves only. Forlongitudinal waves, compressions and rarefactions are used.

•• Amplitude, A, SI Unit: Amplitude, A, SI Unit: metre metre (m)(m)– The maximum displacement from the rest or central position, in either

direction.

Describing Waves•• PhasePhase

– Two points (such as x &x’, and y & y’) are said to be inphase because that are moving in the same direction with thesame speed and having the same displacement from the restposition. Any two crests or trough are in phases.

Describing Waves•• Wavelength, Wavelength, λλ, SI Unit : , SI Unit : metre metre (m)(m)

– The shortest distance between any two points on a wave thatare in phase. The two easiest points to choose for a distanceof one wavelength are two successive crests or troughs.

Describing Waves•• Frequency, Frequency, f, f, SI Unit: hertz (Hz)SI Unit: hertz (Hz)

– The number of complete waves produced per second. The figure showstwo complete waves and if they are produced in one second, then thefrequency of this wave is two waves per second or 2 hertz.

•• Period, Period, TT, SI Unit: second (s), SI Unit: second (s)– The time taken to produce one complete wave. T = 1/f

Describing Waves•• Wave SpeedWave Speed, , vv, SI Unit : , SI Unit : metre metre per s (m/s)per s (m/s)

– The distance travelled by a wave in one second.•• Wave FrontWave Front

– An imaginergy line on a wave the join all points which have the samephase of vibration.

The Wave Equation

The relationship of v, λ & f

!fv =

The relationship of v, λ & TSince T = 1/f

Tv

!=

v = fλf = v/ λλ= v /f

f = 1/Tv = λ/Tλ= vTT = 1/fT = λ/v

λf

v

Tv

λ

Worked Example 1A transverse wave is found to have a distance of 4 cm from atrough to a crest, a frequency of 12 Hz, and a distance of 5 cmfrom a crest to the nearest trough. Determine the amplitude,period, wavelength and speed of such a wave.

Solution:Amplitude = 4 cm / 2 = 2 cm

Period, T = 1/f = (1/12)s = 0.083 s

Wavelength, λ = 5 cm x 2 = 10 cm = 0.1m

Speed, v = f λ = (12 x 0.1) m/s = 1.2 m/s

Worked Example 2Two boats are anchored 4 metres apart. They bob up and downevery 3 seconds, but when one is up the other is down. There arenever any wave crests between the boats. Calculate the speed ofthe waves.

Solution:

Period, T = (3 x 2) s = 6 s

Wavelength, λ = 8 m

Speed, v= λ/T = (8/6) m/s = 1.33 m/s

The Ripple Tank (WavesProduction)• The Structure

– A shallow glass-bottomed tray;– A light source directly above

the tray; and– A white screen beneath the

tray used to capture theshadows formed when waterwaves traverse the tray.

• Production of waves– Plane waves by using the

straight dipper– Circular waves by spherical

dipper

Web References

Wave MotionPhysics Classroom on WavesIntroduction to WavesApplets