WAVESWAVESPhysics Notes

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WavesWaves• Waves are repeated to-and-fro vibrations that

transfer energy away from an energy source

Describing wave Describing wave motionmotion

Term Description SI units

Amplitude, A

The maximum displacement of the rope from the rest position

Metre (m)

Wavelength, λ

The shortest distance between 2 successive crests or troughs

Metre (m)

Frequency, f The number of complete waves produced per second

Hertz (Hz)

Period, T The time taken to produce one complete wave

Second (s)

Wave speed, v

The distance travelled by a wave in 1 second

Second (s)

Describing wave Describing wave motionmotion

trough

crest

Types of WavesTypes of Waves• Transverse waves

o The vibration of the particles in the medium is perpendicular to the direction in which the wave travels

o Eg. water waves, rope waves, all types of electromagnetic waves including light waves, microwaves, X-rays, gamma rays

o The highest point reached by a vibrating particle in a transverse wave is called crest or peak while the lowest point is called trough

• Longitudinal waveso The vibration of the particles in the medium is parallel to the direction

in which the wave travelso Eg. sound waveso The section in which the vibrating particles in a longitudinal wave are

closest together is called compression while the section in which the vibrating particles are furthest apart is called rarefaction

Longitudinal and Longitudinal and Transverse wavesTransverse waves

WavefrontsWavefronts• Any line or surface over which all the vibrating

particles are in the same phase• Particles in the same phase have the same speed

and are at equal distances from their source• In transverse waves, wavefronts are normally

lines joining all the peaks at equal distance from their source

• The distance between successive wavefronts equals a wavelength

• The direction of travel of a wave is always perpendicular to its wavefronts as indicated by lines drawn perpendicular to the wavefronts.

WavefrontsWavefronts

Wave EquationWave Equation• Velocity of wave, v = fλExample: The speed of light in vacuum is 3 x 108

m/sCalculate the frequency of orange light, given that

its wavelength in vacuum is 6 x 107 m.

3 x 108 = f x 6 x 10-7

f = (3 x 108)/(6 x 10-7) = 5 x 1014 Hz

Ripple TankRipple Tank• The properties of waves in general and water waves

in particular are most easily studied in a ripple tank

Reflection of wavesReflection of waves• Waves are reflected when an obstacle is placed in

their paths• All reflected waves obey the law of reflection

which stateso The angle of reflection equals the angle of incidenceo The incident wave, the reflected wave, and the normal all lie on the

same plane

Properties of reflected Properties of reflected waveswaves

• The reflected wave the same wavelength, frequency, and speed as the incident wave

• The velocities of the reflected and incident waves are different because they travel in different directions

• The angle of reflection equal to the angle of incidence

Refraction of wavesRefraction of waves• Waves are refracted when their speeds are changed• The speed of a wave is changed when the wave

moves from a dense medium into a less dense medium or from deep water to shallower water

• If the incident wave is travelling along the normal, it will continue to travel along the normal after entering water of a different depth

• In all other cases, refraction produces a change in wave direction

• On entering shallower water, the wave direction bends towards the normal.

• On entering deeper water, the wave direction bends away from the normal

Refraction of water Refraction of water waveswaves

Refraction of wavesRefraction of wavesProperties Shallower to deeper

waterDeeper to shallower water

Wavelength Increases Decreases

Frequency Unchanged Unchanged

Speed Increases Decreases

Velocity Increases Decreases

Direction of travel Bends away from normal

Bends towards normal

Ripple Tank to show Ripple Tank to show refraction of wavesrefraction of waves

SoundSound• Production of sound waves by vibrating

sources: sound is produced by vibrating sources (eg tuning fork) placed in a medium (solid, liquid, gas)

• Nature of sound waveso It is a form of energy that can be transferred from one point to

anothero It is an example of longitudinal waves consisting of

compressions and rarefactionso Compressions are regions where air pressure is slightly higher

than he surrounding air pressureo Rarefactions are regions where air pressure is slightly lower

than the surrounding air pressure

Sound wavesSound waves

Range of audible Range of audible frequencyfrequency

• The range of frequency that a human ear can detect is from 20 Hz to 20,000 Hz

Transmission of sound Transmission of sound in a mediumin a medium

• Sound waves require a medium for transmission• Sound waves cannot travel through a vacuum

Vacuum jar

Speed of sound in Speed of sound in solid, liquid, gassolid, liquid, gas

Medim Speed in m/s

Air (gas) 300

Water (liquid) 1500

Iron (solid) 5000

Speed of sound changes with changes in temperature or humidityChange in Explanation

Temperature Sound travels faster when temperature rises

Humidity Sound travels faster when humidity increases

Pressure A change in pressure does not affect speed of sound

Experiments to Experiments to determine speed of determine speed of

sound in airsound in air• Pistol method

o Observer A and B are positioned at a distance s apart and with a measuring tape, measure and record s. (must be more than 1km)

o A fires a starting pistolo B starts the stopwatch on seeing the flash of the pistol and

stops the stopwatch when he hears the soundo The time t, is recordedo The speed of sound v can be calculated by

• Speed = distance / time

• For better accuracy, the experiment should be repeated and the average speed of sound can be calculated.

• The experiment can be repeated by interchanging the positions of A and B so as to minimise the effect of the wind direction.

Experiments to Experiments to determine speed of determine speed of

sound in airsound in air• Echo method

o Observer A and B are positioned at a distance s from the wall and with a measuring tape, measure and record s

o A claps two wooden blocks. o On hearing the echo (reflected from the wall), he repeats the

clapo B starts the stopwatch and also starts counting from zero till

the nth clap. o The time interval tn is recorded

o The average time between successive claps is t = tn/n

o The speed of sound v can be calculated by • speed = distance/time

Reflection of soundReflection of sound• An echo is a reflection of sound• Reverberation is the effect of a prolonged sound

due to the merging of many echoes• Echoes are used in determining the depth of sea

and locations of shoals of fish

Electromagnetic Electromagnetic spectrumspectrum

• The entire possible range of electromagnetic waves is called the electromagnetic spectrum

Properties of Properties of electromagnetic waveselectromagnetic waves• They are generated by accelerating charged

particles• They travel at 3 x 108 m/s in vacuum• They obey the laws of reflection and refraction• They show wave properties such as diffraction

and interference• They obey the equation v = fλ• They are progressive transverse waves carrying

energy in the form of oscillating electrical and magnetic fields vibrating at right angles to one another and to the direction of travel of the waves

Radiation

Wavelength/m

Sources Detectors Uses

Gamma rays

10-15 – 10-11 Cosmic rays radioactive substances, nuclear changes

G M tubes with counters, bubble/cloud chambers

Checking welds, killing cancer cells in radiology, photography

X-rays 10-13 – 10-8 X-ray tubes: stopping of fast-moving electrons by a heavy metal target

Photographic film, fluorescent screen

X-ray photography, analysis of crystal structure

Ultraviolet

10-8 – 10-7 Mercury vapor lamps, sun, spark discharges

Fluorescent screens/dyes

Forgery detection, sun lamps

Visible light

10-7 Hot bodies, lasers, fluorescent screens, sun

Photographic film, photodiodes

Chemical spectral analysis, fibre optics

Infra-red 10-7 – 10-3 Warm bodies, sun, fires, furnaces

Blackened thermometers, thermocouples

TV remote control, radiant heaters

VHF and UHF (TV) waves

10-4 – 10-1 TV transmitters Aerials and TV sets

Communications, entertainment

Radio waves

10-3 – 103 Radio transmitters

Aerials and radio sets

Radio, telescope, radar, communications