Wave MotionProgressive Waves

There are two basic types of wave motion. Waves are known as either “transverse” or “longitudinal” depending on their motion. Both types are known as progressive (travelling) waves because they involve a disturbance moving away from a source into surrounding areas. When this happens energy is always transferred from one point to another.

Transverse Waves

Transverse waves are those waves in which the disturbance of the medium is perpendicular to the direction in which the wave is moving. These are commonly seen in water, ropes and springs.

A simple transverse pulse is seen when one end of a piece of rope or string is moved up and down in a direction perpendicular to its length. If the rope starts off in the mid position and moved up, down and back to the string position, one complete wave pulse is generated. The rope shows a peak and trough which travel in a certain velocity.

A simple transverse waves is seen when pulses are generated continuously. The particles of the rope move up and down around a fixed central position, but the wave travels down the rope away from the source. The rope shows a series off peaks and troughs which travel a certain velocity.

THE TERMINOLOGY OF WAVE MOTION

Any two points in the wave having identical motion are said to be in phase with each other. The distance between two consecutive places in a wave having identical motion is called the wavelength, λ. The wave travels with a certain wave velocity, v. The period, T, of the wave motion is the time for one complete cycle of oscillation. The frequency of the wave, ƒ, is the number of complete wave cycle in one second. ƒ, is therefore equal to 1/T. The amplitude, α, of the wave is the size of the maximum disturbance of the medium in which the wave travels.

Longitudinal Waves

Longitudinal waves are those in which the disturbance of the medium is parallel the direction of the movement of the wave. Spring can be used to transmit longitudinal waves. Single pulses or continuous waves may be generated.

Frequency (ƒ)

The Frequency is the number of complete oscillation of the wave in one second and it has the unit Hertz (Hz). It applies to progressive or stationary waves.

Let’s examine the guitar string vibrating. Imagine we have slowed time down so that we are watching the guitar string for only one hundredth of a second.

The string went through 3 cycles in one hundredth of a second. In one second, it would go through 300 cycles. Its frequency of vibration is 300 cycles per second or 300 Hz. One Hz is one cycle, or oscillation, per second.

Velocity (v)

A progressive wave will move forward a distance equal to its wavelength each oscillation. If a wave has a frequency of 10 Hz it would move 10 wavelengths forward in one second. If the wavelength is 2 m the distance traveled by the wave in 1 second would be 10 x 2 = 20m. The distance traveled per second is known as the velocity (v) of the wave in m/s. Therefore, for all travelling waves:

V=ƒλAmplitude (α)

The Amplitude, α, of a wave is the maximum displacement of the particles from their rest position (take note that the distance from a peak to a trough is twice the amplitude).

The amplitude increases is the size of the disturbance of the source increases. The larger the amplitude of the wave the greater the energy transferred by it.

Summary

The period, T, of a wave (or an oscillation) is the time taken in seconds in one complete cycle. It’s the inverse of the frequency of the wave in Hz.

T=1/ƒSo for a wave frequency 10 Hz= 10 complete cycles per second.

In one period the wave will move forward a distance ʎ at a velocity v.

Therefore, v=ƒλSound

Sound Waves

Sound waves are longitudinal waves. The particles carrying the sound vibrate about fixed position parallel to the direction in which the sound travels. This is easily demonstrated with a tuning fork generating a sound wave in air.

The tuning fork vibrates at a fixed frequency; this produces alternate regions of bunched (compressed) and spread-out (rarefied) molecules in air around it.

These compressions and rarefractions are similar to the peaks and troughs in the transverse wave. Individual molecules simply vibrate to and fro, parallel to the direction of the sound wave.

As with transverse waves, the wavelength is the distance between two neighboring parts of the wave having identical motion. These are two consecutive parts of the wave with the same pulse.

Pitch- music and noise

A sound of a particular regular frequency is called a tone or musical note. Music is a combination of these sounds in sequence.

The pitch of a note depends on the frequency of the sound waves reaching the ear, which in turn depends on the frequency of the source of the sound. Musical notes have higher pitch if their frequency is higher.

On a piano, middle C has a frequency of 262Hz. The next higher C has a frequency of 524Hz, double that of middle C. As you might have guessed, the C below middle C has a frequency of 131Hz. Turning forks produce note of a single pure frequency. Musical instruments tend to produce more complex sounds that possess combination of different frequencies. If a sound is composed of irregular, varying frequencies, we describe it as a noise. Humans can hear notes which vary in pitch between a few Hz and about 20 kHz. As people get older the upper frequency which their ear can hear drops considerably. Certain animal can hear notes outside the range of human hearing. Dogs can hear whistle above 25 kHz and bats use their high pitch whistle as a kind of echo reflecting radar to avoid collisions.

Sound waves are reflected well from hard, flat surfaces, such as walls or cliffs and obey the same law of reflection as other waves. Sound which has been reflected in this way is called an echo. The laws of reflection for sound can be verified using cardboard tubes and a sound source such as a ticking watch. The loudness of the sound heard through the receiving tube can be adjusted to be a maximum. At this point it’s found that the angle of incidence is equal to the angle of reflection.

Echoes can be can be used to obtain a reasonable calculation for the speed of sound in air. If someone stand about 50 m from a high wall and claps their hand, they will hear the echo of the sound reflected from the wall. If they keep clapping so that each clap coincides with the echo of the previous one, the sound has travelled to the wall and back again in the same time between two claps.

By timing a number of claps with a stopwatch, and measuring the distance to the wall, a reasonable value of the speed of sound in air can be obtained. The value of the speed of sound in air is 330 m/s .

One the claps were synchronized with the echoes it was found that 66 claps were made in a 20 second period. This means that the echo travelled 100 meters in a time of 20/66= 0.3 seconds. The speed of sound can therefore be measured as 100/0.3 = 330 meters per second.

Knowing the speed of sound allows us to estimate a distance by measuring the echo delay. Suppose the clapping method was use to estimate the distance to a large wall and it was found that 45 claps was made in a 20 second period.

The echo delay is 20/45 = 0.44 second.

If the speed of sound is 330 m/s then the sound will travel 330 x 0.44 = 145 m. in this time. The distance to the wall will be half of this, approximately 73 m.

Sound must have a medium in which to travel. The speed will be different in different materials. If the listener places one ear around the surface of a very long wooden pole and a sharp noise is made at the other end, the sound is received by each ear at slightly different times. The sound travels much faster in the wood and so the ear in contact hears the sound slightly before the other one. Generally, sound travels much faster in solids and liquids (including water) that in air.

The experiment shows an electric bell ringing inside a sealed jar. When the pump is switch on, air is gradually removed from the jar.

What happens to the sound? What does this tell us about the sound

INTENSITY and LOUDNESS of the Sound

For sound to be heard, energy must transfer from the source to the listener. The intensity of the sound wave is defined as the rate of flow of energy per unit area perpendicular to the direction of the wave. The intensity of a sound wave in air is proportional to the density of the air, the square of the frequency of the sound and the square of the amplitude of the sound.

As the density of the air is relatively constant when listening to given sounds, the most important factoring the intensity of the sound of a particular frequency is the square of the amplitude. Consequently, if the amplitude of the vibration of a guitar string is doubled, the intensity of the sound energy generated is not doubled but actually four times as greater.

Note: Double the amplitude, four time the intensity.

The loudness of a sound is measured in decibels (dB). The vey quietest sound that can be heard is around zero decibels (0 dB). The loudness of the sound is related to the varying pressure on the eardrum caused by the sound wave striking it. This varies with the intensity of the wave but our ears are more sensitive to some sounds than others, so there is not a simple relationship between loudness and intensity. Generally speaking the ear is more sensitive to sound of higher frequency. This means that higher notes which have a lower intensity can seem as loud as lower notes of higher intensity.

ULTRASONICS

The human ear cannot detect sound at a frequency higher than 20 kHz. Pressure waves at a higher frequency are said to be at an ultrasonic frequency. Making use of those high frequency pressure waves is referred to as ultrasonic or ultrasound.

ECHO SOUNDERS

As radio waves do not travel far in sea water, ultrasonic pressure pulses are used to measure the sea depth at a particular point. The short wavelengths use help stop the pulse spreading out as it travels, ensuring that enough of the transmitted energy is received so that a time delay can be measured.

ULTRASOUND SCANNING

Pictures of unborn babies are obtained using an ultrasound scanner. This relies on the fact that the pressure waves will pass through the soft tissue surrounding the baby bones. The short wavelengths use allow a reasonably a detailed picture to be obtained.

ULTRASONIC CLEANING

If a cleaning fluid in which an object has been placed is agitated at ultrasonic frequencies, the pressure waves produce a scrubbing action. The result is that the object is cleaned far more thoroughly than would be otherwise possible.

Ripple TanksThe Ripple Tanks is a useful piece of apparatus for demonstrating wave properties.

It consists of shallow rectangular water filled tray with a glass base and an overhead light source. When an object is placed in the water the light passing through the water from the overhead light is disturbed. This disturbance can be viewed on a card placed on the floor. To see this effect more clearly, experiments with a ripple tank should be conducted in a dark room.

Waves can be made in the tank by oscillating an object on the surface of the water. The waves travel away from the object in all directions.

Straight objects make waves with plane waveforms. Round objects make waves with curved wavefronts. The inner sides of the tray have absorbing barriers to minimise reflections.

Waves can be generated in a more controllable way by using small beam of wood suspended from rubber bands so as to just break the water surface. A small motor with an eccentric cam is mounted on the beam which causes it to vibrate when the motor is operating.

Waves travel away from the beam across the surface of the water in the tank. These are known as plane waves as the front of each wave forms a straight line.

It is also possible to create circular waves using the same method. The only difference is that circular object, and not the beam of wood, is in contact with the water`s surface. This is shown in the photograph. Notice that the circular dipper is only just in contact with the water. You will also see that we have used a crocodile clip as our eccentric cam.

By adjusting the speed of the motor, waves of differing wavelength may be generated.

If the motor turns slowly, waves of longer wavelength are produced.

If the motor turns quickly, waves of shorter wavelength are produced.

If we add a stroboscopic light source to the apparatus, measurement of the wave can be obtained.

If the light is flashing at the same frequency as the wave, the shadow will appear to be stationary: This is because the wave travels exactly one complete wavelength between the flashes.

Therefore, If the frequency of the strobe is known, so is the frequency, f, of the wave. We can the measure the wavelength using a ruler. These values are used in the Progressive Waves section to verify the relationship between. V, f,

The ripple tank can be used to demonstrate the main properties which all waves possess. These are reflection, refraction and diffraction.

Reflection

A plane wave strikes an angled barrier. The reflected wave can be seen moving to the left

Refraction

A plane wave travels over an angled obstacle. The wave gets refracted twice, once away from the normal when meeting the obstacle and then once towards the normal when leaving the obstacle.

Diffraction

A plane wave strikes a barrier with a small gap in the middle. A small part of the wave is allowed to pass through the hole and diffracts into a circular wave. This wave is very weak as it only has a small part of the original wave`s energy.

By using the riffle tank the wave property of a reflection can be demonstrated. A straight barrier is placed in the path of some plane waves. The waves are reflected at the barrier and move in a new direction. They remain plane waves after reflection.

All types of waves may also be reflected. Sound waves can reflect from walls or buildings. In this way sound can reach places indirectly.

Light waves also reflect off many surfaces. In all cases the waves move off in a new direction after striking the reflecting surface.

The Terminology of Reflected Waves

Waves striking a reflective surface are called incident waves. Waves reflected from a surface are called reflected waves. A line perpendicular to the surface at the point of reflection is called a normal. Incident waves may meet the surface any angle. The angle between the normal and the direction of motion of the wave at the boundary is called the angle if incidence (i). The angle between the normal and the direction of motion of the reflected wave is called the angle of reflection (r).

By making the reflecting surface curved, It`s possible to focus the incident wave. The effect is demonstrated by using the curved reflective barrier shown here in the photograph.

The barrier is causing the wave`s energy to be concentrated at a point (the focus).The same principle is used to focus electromagnetic waves transmitted by television satellite.

Refraction

Refraction is the change in the direction of a wave when its velocity changes at a boundary, this gives rise to a corresponding change in the wavelength of the wave, but the frequency remains unchanged.

In the ripple tank this may be shown by changing the depth if the water in one region of the tank, and allowing waves to pass into this region at an angle.

The waves change direction when passing into the shallow region (different medium). In this case the waves travel more slowly in the shallow region, and this causes them to be refracted at the boundary between the two.

If the waves pass into a curve-shaped region of shallower water, then they can be shown to converge.

This is achieved by putting a suitably shaped piece if glass into the tank.

The same effect occurs when light waves pass through a glass lens.

Light waves slow down when they enter glass, just as water waves slow down when they enter a shallow region. Refraction occurs in light in a similar manner.

If a beam (ray) of light passes through a rectangular glass prism with its sides perpendicular to the beam, the light appears to pass straight through, unaffected by the glass.

If the glass block is rotated so that the light strikes the side of the block at an angle, the beam is refracted as it enters the block and also as it leaves it.

The terminology of Refracted Waves

Waves moving from one medium to another and meeting a boundary are called incident waves.

Waves moving from one medium to another and leaving a boundary are called refracted waves.

A line perpendicular to the boundary between the two media is called a normal. Incident waves may meet the boundary at an angle. The angle between the normal and the direction of motion of the wave at the boundary is called the angle of incidence. The angle between the normal and the direction of the motion of the refracted wave is called the angle if refraction.

The light is refracted at both surfaces. There are therefore two angles if incidence and refraction as the light passes through the block, one at the first surface as it enters the block and the other at the second surface as it leaves it. Both are measured from their respective normal.

In this case the light is refracted towards the normal on entering the block, and away from the normal on leaving it.

On entering the glass, the angle of incidence is greater than the angle of refraction.

On leaving the glass the angle of incidence is less than the angle of refraction.

Diffraction

Diffraction is the property exhibited by waves when they encounter an edge or passing through an aperture, such as a hole or slit.

When diffraction occurs, the direction of propagation and the shape of the wave may change.

If plane water waves meet an aperture in a barrier, diffraction effects are observed.

If the aperture is large compared to the wavelength of the waves, a small effect may be seen at the edge if the wave after passing through the aperture. The edges of the wave become very slightly curved. This is known as edge diffraction.

If the wavelength of the waves is about the same size as the aperture, much more noticeable diffraction occurs. The waves emerge from the aperture with a curved wavefront. They spread out in all direction with an apparent centre at the aperture. This is often referred to as single slit diffraction.

Light may be diffracted in a similar way to water waves.

If a narrow parallel beam of light falls on a wide aperture, the edge diffraction effect in negligible. The light continuous in its straight lines after the aperture and can be made to fall on a screen, with no apparent edge diffraction being visible to the naked eye.

If light passes through very narrow slits, diffraction effects can be demonstrated. As the wavelength of light is very small, around 500 nanometres, the diffraction effects are not noticed in everyday observations of the behaviour of light. They can, however, be demonstrated in the laboratory using laser and very fine optical slits or diffraction gratings.

Interference

When two spherical are attached to the oscillating beam in a ripple tank, both will produce circular progressive (travelling) waves on the water surface.

As they are created by the same vibrating source, these two sets of waves are coherent – similar in amplitude, wavelength and phase.

As they progress through the tank they overlap, When this occurs the two sets of waves interfere with each other.

When two wavefronts meet, at some point in the tank they are exactly in phase with each other. These are known as antinodes. At this point interference occurs and the amplitude of the wave is doubled.

At the other point in the tank called nodes the two wavefronts meet exactly out of phase with each other and they cancel each out by destructive interference.

The diagram shows two circular progressive waves which are coherent.

Where two waves of the same type meet they combine to give twice the amplitude. This point is called an antinode. The red dots on the diagram indicated antinode.

At the point where a trough meets a crest, cancellation occurs. This point is called a node. The blue dots indicate nodes.

The arrows show that the channels of nodes and antinodes form. The faint channels are where nodes are placed and cancellation has occurred.

EarthquakesThe Earth`s Crust

The outer layer of the earth (the crust) is not continuous. In fact it`s made up of several separate plates. Each of these plates is about 100 km thick and they move relative to each other.

The line where two plates meet is called a fault. If two plates next to other move, an earthquake occurs at the fault.

Earthquakes and Seismic Waves

In an earthquake massive quantities of energy are released by the sudden movement of part of the earth`s surface. At the source of the earthquakes this often involves damage to roads, buildings and other structures due to the extent of the movement

When the earthquake occurs, some of the energy released is in the form of waves which radiate away from the source as it fractures. These seismic waves are essentially sound waves which travel through the earth`s surface and may contain up to 10% of the energy released during the earthquake.

There are two types of Seismic Waves.

1. Longitudinal waves, known as Compressional or Primary (P) waves. These vibrate the ground in the direction of motion of the wave. They travel the fastest, at speeds between 1.5 and 8 kilometres per second in the earth`s crust.

2. Transverse waves, known as Shear or Secondary (S) waves. These vibrate the ground at right angles to their direction of motion. They travel more slowly, usually at around 60% to 70% of the speed of the P waves.

Seismic waves may be detected by an instrument known as a seismograph. This device has a heavy weight fixed to form a type of pendulum.

When the earth shakes, the base and frame of the instrument move, but the inertia of the heavy weight tends to keep the pendulum in place. The

pendulum and its frame therefore move relative to each other and this movement is recorded over time as a seismograph.

Seismograph stations exists at many places on the earth , with instrument set up to record north-south, east-west and vertical displacement of the ground.

Test your knowledge by filling in the graphs in the following text.

Although the speeds of the Primary (P) and Secondary (S) waves vary at different parts on the earth`s surface, the ratio between the speed of the P wave and that of its following S wave is relatively constant. This fact enables us to make reasonable calculations of where the earthquake occurred from seismograms made at different measurement stations.

If a P wave travels at 10 kilometres per second from the source of the earthquake it will be detected by a seismograph located 300 km away ____ seconds after the earthquake occurs.

If the S wave from the same earthquake is travelling at 60 % of the speed of the P wave, it will have a speed of ____ km/s.

This means it will reach the same seismograph ____ seconds after the earthquake.

Therefore at a point 300 km from the earthquake the Primary and Secondary waves arrive ____ seconds apart.

What will be delay between the P and S waves at a point 1500 km from the source of the earthquake? ____

Using similar data from a different earthquake, we can see that waves from the particular earthquake travel to three different observation stations, as shown:

The ratio between the distance from the source and the S-P delay is constant at 12:1.

This gives a quick and reasonably accurate estimate of the distance of the epicentre of the earthquake from the observation station which detects it. If the S-P delay in seconds is multiplied by the factor of 12 km/s the approximate distance in kilometres will be obtained.