Waves and wave motion. In physics, waves are classified as

either mechanical waves or electromagnetic waves.

Examples of mechanical waves include, water waves, waves on a rope or slinky and sound waves. All mechanical waves must have a medium to travel through.

Electromagnetic waves make up the electromagnetic spectrum and include radio waves, micro-waves, visible light and infra-red waves. Electromagnetic waves do not require a medium to travel, they can travel through a vacuum, at a speed of 3 x 108 m/s.

Travelling mechanical waves.

“ a travelling mechanical wave is a disturbance carrying energy through a medium without any overall motion of that medium”.

Waves can be seen as a means of transferring energy from one place to another.

Periodic waves.

A disturbance in a medium caused by a series of identical wave pulses is known as a periodic wave.

Transverse and longitudinal waves.

A transverse wave is a wave where the direction of the vibration is perpendicular to the direction in which the wave travels. (e.g. waves on a rope, water waves, E.M. waves)

A longitudinal wave is a wave where the direction of vibration is parallel to the direction in which the wave travels. (e.g. compressions on a spring, sound waves)

Terms used to describe periodic travelling waves.

The top of the wave is called a crest, the bottom of the wave is called a trough.

The maximum distance of any particle of the medium from the undisturbed position is called the amplitude (A). Measured in metres.

The disturbance produced by one complete vibration of the source is called an oscillation or cycle( i.e. one crest and one trough.)

The distance from any point on one cycle to the corresponding point on the next cycle is called the wavelength () i.e. trough to trough or crest to crest. Measured in metres.

Vibrating source

The number of cycles passing a point per second is called the frequency ‘f’ of the wave. Frequency is measured in units called hertz (Hz).

1 Hz = 1 cycle per second.

The distance travelled by any point on the wave in one second is the velocity of the wave ‘c’, measured in metres per second.

c = fλ

Wave phenomena

Reflection Refraction Diffraction Interference Polarisation The Doppler Effect.

When discussing thevarious propertiesof waves, we will use theidea of wave fronts.

Wave fronts are a series of parallel lines drawn to represent a number of waves. The parallel lines are drawn to represent the position of an advancing wave. The lines are formed by joining points that are in phase, such as the crests.

Reflection of waves.

When a wave front strikes an obstacle, it is reflected.

The angle of incidence equals the angle of reflection.

i° = r ° i r

N

Refraction of waves.

When waves travel from one medium to another, they change speed.

If the waves passes the inter-face at an angle other than 90 ° then the wave will be refracted.

Refraction is the change in direction of a wave as it passes from one medium to another.

Diffraction of waves

When a wave front strikes an obstacle or a gap, it tends to spread out in the region behind the obstacle or gap..

The extent to which the wave spreads out depends on the size of the obstacle or gap in terms of the wavelength ‘λ’ of the wave.

The greater the wavelength of the wave compared to the width of the obstacle, the greater the extent to which the wave spreads out.

The diffraction of sound waves explains why an open door will allow a noise form outside to be heard throughout the room. As the sound wave passes through the opening of the door, it is diffracted and spreads out in all directions behind the door.

Diffraction is the spreading out of a wave when it meets an obstacle or gap in its path.

When a wave passes through a narrow gap it is diffracted and spreads out. For a wave of a given wavelength, the narrower the gap through which the wave passes, the greater the diffraction will be.

Polarisation of waves.

Polarisation occurs when the plane of vibration of a wave is restricted to one plane only.

Only transverse waves can be polarised.

Vertically Horizontallypolarised polarised.

All electromagnetic waves, including visible light are made up of an electric component and a magnetic component which vibrate at right angles to each other. A source of white light will consist of a number of waves vibrating in all directions. Polaroid sunglasses work by coating the lenses of the glasses with a material which will only allow light of one plane of vibration to pass through. All other waves are absorbed. Light which has been polarised in such a way is said to be plane polarised.

If two pieces of polaroid material are held perpendicular to one another, no light can pass through.

Light Source

Polaroid A Polaroid B

Interference of waves.

What happens when two or more waves meet at a point ?

Answer: The resultant displacement at that point is equal to the algebraic sum of the individual displacements at that point. (Principle of superposition)

If waves from coherent sources meet and interfere with each other an interference pattern is produced.

Coherent sources are sources which have the same frequency and are in phase with each other.

Interference occurs when two or more waves meet. The amplitude of the resulting wave is equal to the algebraic sum of the amplitudes of the interfering waves.

Depending on the point at which waves meet and interfere, the resultant amplitude will either be greater or less than the initial amplitudes.

Constructive interference occurs when two waves meet and the amplitude of the resulting wave is greater than the amplitudes of the individual waves.

Destructive interference occurs when two waves meet and the amplitude of the resulting wave is less than the amplitudes of the individual waves.

Interference patterns.

If two or more coherent waves meet and interfere, then an interference pattern is produced.

Diagram shows the interference pattern produced in a ripple tank, by two coherent point sources.

The Doppler Effect.

The Doppler Effect is the apparent change in frequency due to the relative motion between source and observer.

For sound waves the Doppler effect produces a change in pitch.

For light waves a change in colour is produced.

Stationary and moving source.

A B A BS S1 S2 S3

Crest 1

Crest 2

Crest 3Crest 3

Crest 2

Crest 1

A stationary source S emits a wave of given wavelength and frequency. The wave is emitted in all directions from a point source, with equally spaced wave frontsmovie

A moving source S emits a wave of given wavelength and frequency. The emitted wave fronts are no longer equally spaced but begin to ‘bunch up’ in front of the moving source.

For a stationary observer in front of a moving wave source (source and observer moving closer), the wavelength of the wave appears to be decreasing.

The speed ‘c’ of the wave remains constant.

The frequency appears to be increasing.

f’ = f c c - u

For a stationary observer behind a moving wave source (source and observer moving apart), the wavelength of the wave appears to be increasing.The frequency appears to be decreasing. f’ = f c c + u

where, f ' = observed frequency f = actual frequency at sourcec = speed of the waveu = speed of the source or observer

Examples of the Doppler Effect.

Any moving source of sound or light waves will produce the Doppler Effect for a stationary observer. The faster the source is moving, the greater the effect.

Formula 1 racing cars, passing ambulance or fire engine.

Applications of the Doppler Effect include Garda speed guns and the Red Shift of stars.

Standing (stationary) waves.

If a rope is fixed at one end and vibrated at the other, a wave is produced and travels along the rope. When this wave meets the fixed end it is reflected and travels back along the rope.

If a second wave has been produced it will meet and interfere with the reflected wave.

At particular frequencies of vibration a standing wave is produced on the rope.

The rope appears to have points of maximum vibration and points which appear to be at rest.

Terms used to describe standing waves.

A standing wave is produced when two coherent waves of the same amplitude but travelling in opposite directions meet.

A point of maximum displacement (caused by constructive interference), is called an anti-node.

A point of no displacement (caused by destructive interference), is called a node.

anti-node

node

Inter-nodal distance

For a standing wave, the distance from one node to the next is equal to half a wavelength.

The distance from an anti-node to the next anti-node is half a wavelength.

Node to anti-node is one quarter wavelength.

Λ/2 λ/2

Sound as a wave motion.

Every sound is produced by a vibrating source.

The vibrating source causes air molecules to vibrate and the vibration travels from air molecule to air molecule.

When this vibration causes the ear drum to vibrate, the human ear detects the vibration as a sound.

The human vocal chords vibrate to produce the sound of your voice.

Sound travels as a longitudinal wave.

Sound waves can undergo all of the wave phenomena such as reflection, refraction, etc…

Sound must have a medium in which to travel, sound cannot travel in a vacuum.

If the air is removed from the bell jar the sound of the ringing bell fades although it continues to ring..

The bell jar experiment!

Reflection of sound.

The existence of echoes verifies the fact that sound can be reflected, when it strikes an obstacle.

The reflection of sound waves in large halls or arenas can enhance the production of sound or make it very difficult to hear.

The study of the reflection and absorbance of sound waves is called acoustics.

Refraction of sound. Refraction is the changing of direction of waves on

entering a different medium, due to a change in speed. When sound waves travel from air of one temperature to

air of a different temperature, they can be diffracted. Sound travels faster in warm air than in cold air. On a warm day sound waves are diffracted upwards

since the waves travel faster in the warmer air closer to the ground.

On a cold day, the waves closer to the ground travel slower and so the waves are refracted downwards.

This refraction of sound waves explains why sounds can be heard more clearly on a cold night.

Diffraction of sound.

Sound waves can be diffracted when they meet and obstacle with a gap in it, such as a wall with an open door or window.

Sound can pass through an open door and spread out into the region behind the open door.

Because of the diffraction of sound, it is possible to hear around corners.

Note: The width of doorways and windows is close to the wavelength of audible sounds, and so the diffraction is considerable.

Interference of sound.

To demonstrate that sound travels as a wave it can easily be shown to undergo both diffraction and interference.

To demonstrate the interference of sound.

Set up the apparatus as shown. Turn on the signal generator. Walk slowly form A to B. The loudness of the sound can

be heard to increase and decrease regularly while moving from A to B.

This is because of the coherent sources producing both constructive and destructive interference between A and B, producing an interference pattern.

Interference produced is evidence that sound is a wave.

Signal generator

Loudspeakers.

Reduction of noise by destructive interference.

Large background noises such as those produced by exhaust systems or air conditioning units can be greatly reduced using destructive interference.

A sample of the problem noise is picked up by microphone and a sound wave of the same frequency and amplitude is produced electronically.

The crests of this wave coincide with the troughs of the noise and the troughs of the wave coincide with the crests of the noise.

The wave is then emitted by loudspeaker into the region where the noise exists and destructive interference occurs.

The noise can thus be eliminated and a region of almost silence is produced.

Speed of sound.

The speed of sound depends on the medium through which sound travels.

In general sound travels faster in a denser medium.

In a gas such as air, the speed of sound increases with increasing temperature.

The change in the speed of sound as it passes from cooler air to warmer air causes refraction and explains why sound can be heard more clearly on a cold night than on a warm day.

Material

Approx speed of sound.

(m/s)

Air (0°C)

Water

Copper

Steel

331

1500

3400

4800

Temperature

(°C)

Approx speed of sound.

(m/s)

0

20

100

331

344

384

Characteristics of notes.

Vibrating objects will often produce sounds with frequencies which are multiples of a given frequency. These frequencies are called overtones.

If ‘f’ denotes a given frequency, then ‘2f’ is the first overtone, ‘3f’ the second overtone, etc…

The main characteristics of a note are loudness, pitch and quality.• The loudness of a given note depends on the amplitude of the

wave producing it. The greater the amplitude the louder the note.

• The pitch of a given note depends on the frequency of the wave producing it. The higher the frequency, the higher the pitch.

• The quality of a note is what distinguishes the same note played on two different instruments.

• The quality of a given note depends on the number and strength of overtones which an instrument produces. Different instruments produce different overtones. A tuning fork or a signal generator can produce a pure note of just one frequency.

Frequency limits of audibility.

For a sound wave to be audible its frequency must be between 20Hz and 20,000 Hz.

The upper limit decreases with age.

Frequencies above 20,000 Hz are called ultrasonic and cannot be heard by humans.

Dogs and bats can hear sounds up to 35,000 Hz.

Natural frequency and resonance.

An object that is free to vibrate will tend to do so at a preferred frequency, called its natural frequency of vibration.

If a periodic force is applied to a vibrating body, with a frequency close to or near to the natural frequency of vibration of the body, the body will vibrate with a very large amplitude.

This phenomenon is called resonance.

Resonance is the response of a body to a frequency equal to or very close to the natural frequency of vibration of the body.

Pushing a child on a swing is an example of resonance. The child must be pushed at a frequency close to the natural frequency of the swing, in order for the child to swing higher and higher.

Resonance.

The frequency of a pendulum depends on its length. Barton’s pendulums can be used to demonstrate resonance.

Opera singers can produce high pitched notes which resonate with a drinking glass and cause it to shatter.

The wire on a sonometer can be made to resonate with a given tuning fork.

Building can collapse due to resonance produced by earthquakes.