The general types and properties of WAVES - an introduction

ripple tank experiments illustrating reflection, refraction and diffraction, all of these are explained with lots of diagrams

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

INTRODUCTION to waves

 Be able to describe that waves transfer energy and information without transferring matter.

 When your TV receives the signal its just coded data in the electromagnetic wave, no material substance arrives!

 However, energy itself must be transmitted or no effected could be produced by the TV receiver!

 Similarly, when ripples on water cause floating objects to bob up and down, energy is needed to do this, but neither the floating object or the water itself actually move in the direction of the transverse waves.

 The most dramatic transfer of energy involves earthquake waves, both transverse and longitudinal, yet the effects are transmitted and felt miles from the epicentre and no part of the earth's crust moves in the direction of the seismic waves but it may move violently from side to side, up and down or compressed/decompressed.

 When sound waves vibrate your ear drum no air moves from the TV, person or musical instrument etc., yet energy is transferred through the medium of air, otherwise, what causes your ear drum to vibrate!

You need to know the two formulae for waves relating them to wavelength, frequency, speed and distance travelled.



Know the differences between longitudinal and transverse waves by referring to sound, electromagnetic and seismic waves.

You need to understand that in a transverse wave the oscillations are perpendicular (at 90o) to the direction of energy transfer, but in a longitudinal wave the oscillations are parallel to the direction of energy transfer ie direction of forward wave movement.

Shaking a slinky spring from side to side produces a transverse wave, as ripples on water and all electromagnetic radiation.

Pulling and pushing on a slinky spring produces pulses of energy transmitted as a longitudinal wave like a sound wave travelling through a medium ie the 'compressions' and 'rarefactions' are in the same direction as the wave movement.

Seismic waves e.g. from earthquakes (form of tectonic activity) can be of both types of wave.


General properties of waves

Introduction - everyday examples of waves

A wave can be described as a regular disturbance that transfers energy. This uniform pattern of movement allows the wave to transfer energy in various forms at a particular frequency. To transfer this energy the particles vibrate or the bulk material oscillates in some way, but the particles or material stay in the same place - only the energy 'moves'!

This description is fine for example ..

When you drop a stone in a pond you see ripples on the surface of the water as the kinetic energy of the impact is transferred in all directions as water waves. If the ripple meets a floating object, that object just bobs up and down as the ripples pass by - the object is not carried along. This is an example of a transverse wave, the vibrations/oscillations at 90o to the direction of wave movement - more details later.

When you play a musical instrument the sound of the notes, that is the energy of the vibration (string or reed etc.), is transferred to your ear by the particles of air vibrating-oscillating to and fro in line with the direction of the sound wave is travelling - this is an example of a longitudinal wave - more details later. The air does NOT move along, only the sound energy is transferred.

However this description of waves doesn't completely fit electromagnetic radiation e.g. visible light, uv, ir, X-rays etc. In this case the energy is carried by photons, which have wave properties, but they do actually move from one place to another e.g. the Sun to Earth or reflected light by which you see objects. The two examples above required a medium e.g. air or water, but electromagnetic radiation can travel through a vacuum as well as transparent materials like air, water or glass. However, the vibrations-oscillations of the photons due to their wavelike properties occur at 90o to the direction of travel, so they are transverse waves.

 

The technical description and properties of a TRANSVERSE WAVE

The above diagram gives an idea of a transverse wave where the oscillations/vibrations are at 90o to the direction the wave moves.

Expressing this another way - the disturbance of the medium is at 90o to the direction the wave is travelling.

e.g. electromagnetic radiation waves, ripples-waves on water, shaking a slinky spring or rope from side to side, earthquake waves of the S-waves type.

  • You should know, understand and be able to use the terms frequency, wavelength and amplitude of a wave in terms of this diagram of a transverse wave.

    • The top of the wave form is called a crest and the bottom of the wave is called the trough see wave diagram above.

    • The wave amplitude = distance from the baseline of zero displacement (rest position) to the point of maximum displacement (to top of crest or to bottom of trough) - see wave diagram above.

    • One wavelength (m) = distance of one complete cycle or oscillation/vibration = horizontal distance from any point on the wave until where it begins to repeat = distance between two crests = distance between two troughs etc. - see wave diagram above.

      • The wavelength is sometimes defined as the distance between the same points on two adjacent/neighbouring disturbances. Both these definitions equate to one complete cycle of the wave oscillation-vibration.

      • Wavelength units are usually metres (m) but other units are commonly used e.g. nanometres (nm, 10-9 m).

    • The frequency of a wave (Hz) = number of complete cycles/oscillations per second = number of complete cycles/waves passing a given point per second.

      • Frequency is measured in Hertz. 1 Hertz = 1 oscillation or vibration/s (1 Hz, 1 per sec or 1 s-1).

    • The period of a wave is the time in seconds for one complete cycle to pass a certain point.

      • wave period (s) = 1 frequency (Hz, s-1)

    • Symbols used: v = velocity, f = frequency, λ wavelength

      • More on calculations based on the equation v = f x λ further down the page.

    • -

 


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The technical description and properties of a LONGITUDINAL WAVE

The oscillations/vibrations of a longitudinal wave are in the same direction as the wave is moving.

The disturbance of the medium is parallel to the direction the wave is moving.

Know and understand why longitudinal waves show areas of compression and rarefaction.

The above diagram shows the compression and decompression (rarefaction) of a longitudinal sound wave, illustrated 'visually' by the pushing pulling of a slinky spring (see below 'picture' below). P-waves are a longitudinal type of earthquake wave.

The 'to and fro' effect is due to the particles of the medium being compressed to give a point of maximum particle density (maximum pressure), squashed up to give a compression. At the same time, further along the wave, the arrangement of particles is stretched out to give a point of minimum density (or minimum pressure) called a rarefaction.

You can appreciate this by the way the vertical lines and spaced out or compressed together.

Also, the diagram above illustrates longitudinal sound waves travelling at the same speed where wave B has twice the frequency and half the wavelength of wave A. You can deduce this because in wave B the distance between two compression or two rarefactions is halved, so twice as many waves will pass a given point in the same time.

The diagram above illustrates a slinky spring 'pulsed' with longitudinal waves. It also illustrates in a way what happens to the air when a sound wave passes through it and the ground with one of the types of earthquake wave (the compressional P waves), which go right through the Earth to the other side of the world!)


Comparing and contrasting examples of transverse and longitudinal waves

  • a) Know and understand that waves transfer energy.

  • b) Know and understand that waves may be either transverse or longitudinal.

    • You need to understand that in a transverse wave the oscillations are perpendicular (at 90o) to the direction of energy transfer, but in a longitudinal wave the oscillations are parallel to the direction of energy transfer ie direction of forward wave movement.

    • Shaking a slinky spring from side to side produces a transverse wave, as ripples on water and all electromagnetic radiation.

    • Pulling and pushing on a slinky spring produces pulses of energy transmitted as a longitudinal wave like a sound wave travelling through a medium ie the 'compressions' and 'rarefactions' are in the same direction as the wave movement.

    • When your TV receives the signal its just coded data in the electromagnetic transverse waves, no material substance arrives! Or does it? Can't photons behave like little bullets?

    • However, if energy itself wasn't transmitted or no effected could be produced by the TV receiver!

    • Similarly, when ripples on water cause floating objects to bob up and down, energy is needed to do this, but neither the floating object or the water itself actually move in the direction of the transverse waves.

    • The most dramatic transfer of energy involves earthquake waves, both transverse and longitudinal, yet the effects are transmitted and felt miles from the epicentre and no part of the earth's crust moves in the direction of the seismic waves but it may move violently from side to side, up and down or compressed/decompressed.

    • When sound waves vibrate your ear drum no air moves from the TV, person or musical instrument etc., yet energy is transferred through the medium of air, otherwise, what causes your ear drum to vibrate!

  • Know that electromagnetic waves are transverse (radio, microwave, infrared, visible light) as are waves on water - eg ripples, sound waves are longitudinal and mechanical waves may be either transverse or longitudinal.

  • Know that all types of electromagnetic waves travel at the same speed through a vacuum (~ empty space) - 'the maximum speed of light' which is 3 x 108 m/s.

  • Know that electromagnetic waves form a continuous spectrum.

    • You should know the order of electromagnetic waves within the spectrum, in terms of energy, frequency and wavelength.

    • You should appreciate that the wavelengths vary from the minute 10-15 metres for extremely high frequency gamma rays to more than 104 metres for very low frequency radio waves.

  • Know that waves are reflected and refracted at boundaries between different materials and in diffraction, can spread out when passing the end of a barrier or through an opening.

  • Know and understand that light waves can be reflected, refracted and diffracted.

  • Appreciate and understand that all three wave effects can be successfully modelled in the way described in the preceding sections above.

 

The general points and behaviour of waves is discussed above and below are dealt with in more detail on separate pages - see the waves index at the end.

 


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More on the general properties and scientific models of waves

(all dealt with in more details for specific examples like light or sound)

All waves undergo reflection, refraction and diffraction and a general description of them is explained below.

Appreciate and understand that all three wave effects can be successfully modelled in the way described in the manner described below and predictions can be made on the basis of these models.

 

What can happens when waves meet a boundary between two media?

When waves meet an interface between two materials there are three possible outcomes.

(i) The wave, its energy, is absorbed by the second material, the energy store of the 2nd material is increased.

Soft materials easily absorb sound wave energy.

Rough matt black surfaces absorb most of visible light that's why they look black!

Infrared radiation from the Sun heats up surfaces.

In these cases you getting minimum wave energy absorbed.

 

(ii) The wave is reflected back off the second material without its energy being absorbed. In this case there is little wave energy absorbed or transmitted.

If the surface is particularly smooth-shiny and flat, very little wave energy is absorbed and you can observe a high quality reflected image e.g. looking at yourself in a silver surfaced mirror!

If the surface is rough, much of the wave energy is absorbed or scattered in all directions.

 

(iii) The wave is transmitted through the second material without being absorbed and the waves may change direction (refraction). This can happen if the material is transparent and the waves can continue passing through the 2nd material

You see this by the 'bent' image at the 'wrong' angle when observed putting a stick in water.

 

(iv) There are situations where waves partially meet a barrier and bend round corners or pass through a gap in a barrier and the spread out - radiating from the gap. These effects are called diffraction and does not involve passing from one medium to another.

You can hear sound round a corner - that's due to a combination of reflection and diffraction effect.

 

REFLECTION of waves

  • Waves are readily reflected off smooth flat surfaces e.g. light reflected off a mirror.

    • Reflection of waves at a smooth surface

    • The vertical dotted line is called the 'normal', it isn't a ray, but helps in the construction and interpretation of ray diagrams. A plane mirror means one of a perfectly flat surface.

    • Angle 2 = angle of incidence of the incident ray.

    • Angle 3 = angle of reflection of the reflected ray.

    • Angle 2 = Angle 3 - the simple 'law of reflection'

    • Angle 1 = angle 4.

    • All angles are measured with respect to the 'normal' which is at 90o to the surface - the dotted line.

    • the 'normal' is an imaginary line at 90o to a surface or a boundary between two media (see refraction below) at a point where the waves are hitting. It is useful when constructing ray diagrams (like the one above) to show the paths of the ways and their angles relative to the surface or boundary.

    • The scientific wave model of reflection.

    • Think of the wavefronts as the crests of the waves e.g. as you observe ripples on water or waves at the seaside.

    • When the waves meet the flat smooth surface they are 'bounced' off symmetrically at the same angle with respect to the normal - see the first reflection diagram.

    • You can readily see this with ripple tank experiment waves - just put a barrier in their way at 45o to their direction and the wave direction is changed by 90o.

    • Similarly you will see the same with light ray experiments using ray box.

 

REFRACTION of waves

  • Waves travel at different speeds in different materials and this can result in a change of direction as the waves pass through a boundary from one material to another.

    • This change in direction at the boundary between two media is called refraction.

  • To explain how waves will be refracted at a boundary in terms of the change of speed and direction, we need diagrams!

    • In fact, a scientific model of waves!

  • The scientific model explaining refraction of waves at a boundary between two media

  • The above diagram illustrates the phenomena of refraction by considering what happens to waves e.g. visible light or water waves.

  • You can think of the parallel lines as representing a series of crests of waves eg think of waves on the sea or ripples in a pond on throwing a stone in or ripple tank experiments in the school laboratory.

  • The vertical dotted line is NOT a wavefront, but as already mentioned in reflection, it is an important imaginary construction line at 90o to the media boundary to help measure what we call the angles of incidence and refraction - see diagram of refraction below.

  • Refraction A: When waves passing through a less dense medium, hit a boundary interface, and enter a more dense medium, the waves 'bend towards the normal' i.e. refraction occurs.

    • *

    • This happens because on entering the more dense medium, the waves are slowed down causing the change in wave direction at the boundary interface. Diagram above and left of diagram below. Diagram B is discussed later, but it is the opposite situation to refraction A.

  • Comparing refractions A and B

  • The above diagram illustrates the scientific model of the wave theory of refraction.

  • You can also see that in refraction A the wavelength is decreased as well as the velocity.

  • The frequency does NOT change.

  • wave speed = frequency x wavelength, in 'symbolic shorthand'    v = f x λ   (see wave calculations)

  • If the frequency (f) does not change, then the velocity (v) is directly proportional to wavelength (λ).

  • The bigger the change in speed the bigger the change in direction - the greater the angle of refraction.

  • You see this effect in ripple tank experiments when you abruptly go from deeper water to shallower water the waves will change direction towards the normal.

    • The waves slow down in shallower water and if they hit the shallower water at an angle, refraction will occur.

    • The waves slow down in shallower water because of increased friction with the bottom surface of the ripple tank.

    • In this example the refraction has nothing to do with density, but is caused by increased friction - increase in the 'drag' effect.

    • You can observe this in a ripple tank by placing a rectangular plate in to the water at an angle to the waves and you can see these changes in wavelength and speed. BUT, by using a stroboscope you can show the frequency does not change.

    • Effect of decreasing speed.

  • For examples see Reflection, refraction and diffraction of visible light, examples with diagrams and explanations

  • Refraction B: When waves from a more dense medium, hit a boundary interface, and enter a less dense medium, the waves 'bend away from the normal' ie refraction occurs.

    • *

    • This happens because on entering the less dense medium, the waves can speed up causing the change in wave direction at the boundary interface. Diagram above and right of diagram below. Diagram refraction A has been previously discussed, but here refraction B is the opposite situation to refraction A.

  • Comparing refractions A and B

  • The above diagram illustrates the scientific model of the wave theory of refraction.

  • You can also see that in refraction B the wavelength has increased as well as the velocity.

  • The frequency does NOT change.

  • wave speed = frequency x wavelength, in 'symbolic shorthand'    v = f x λ  (see wave calculations)

  • If the frequency (f) does not change, then velocity (v) is directly proportional to wavelength (λ).

  • The bigger the change in speed the bigger the change in direction - the greater the angle of refraction.

  • You see this effect in ripple tank experiments when you abruptly go from shallower water to deeper water the waves will change direction away from the normal.

    • The waves speed up in deeper water and if they hit the deeper water at an angle, refraction will occur.

    • The waves speed up in deeper water because of decreased friction with the bottom surface of the ripple tank.

    • In this example the refraction has nothing to do with density, but is refraction caused by decrease in friction - reduction of the 'drag' effect.

    • You can observe this in a ripple tank by placing a rectangular plate in to the water at an angle to the waves and you can see these changes in wavelength and speed. BUT, by using a stroboscope you can show the frequency does not change.

    • Effect of increasing wave speed

  • For examples see Reflection, refraction and diffraction of visible light, examples with diagrams and explanations

  • If the waves hit the interface at an angle of 90o (perpendicular) to the interface between the two mediums, there is still a change in speed and wavelength, but there is NO change in direction, NO refraction and the wave frequency remains the same. See diagrams below where the waves strike the boundary along, or parallel to, the normal.

  • A: When the waves pass from a less dense medium to a more dense medium the waves decrease in velocity at the media boundary and the wavelength also decreases.

  • B: When the waves pass from a more dense medium to a less dense medium the waves increase in velocity at the media boundary and the wavelength also increases.

  • In both cases the frequency remains unchanged and in both cases no refraction takes place.

  • You can observe this in a ripple tank by placing a rectangular plate in to the water parallel to the waves and you can see these changes in wavelength and speed. BUT, by using a stroboscope you can show the frequency does not change.

  • The effect of increasing or decreasing friction in a ripple tank - effectively decreasing speed and wavelength or increasing speed and wavelength,

 

DIFFRACTION of waves

  • The scientific model of the diffraction of waves through a gap (or bending round a corner)

  • Diffraction is the effect of waves spreading out when passing through a gap or passing by a barrier. In effect, waves go round corners! and it doesn't matter if its sound, light or water waves - they all diffract and bend round corners! The effect is so small with light (tiny wavelength), you don't notice it, but you see water waves bending around the the walls of a harbour and you can hear sounds from round a corner.

  • You should appreciate that significant diffraction only occurs when the wavelength of the wave is of the same order of magnitude as the size of the gap or obstacle.

  • A: There is a relatively small diffraction effect when waves pass through a wide gap that is much bigger than the wavelength of the wave.

  • B: You get the maximum spreading or diffraction when the waves pass through a gap of similar size to the wavelength of the incident waves.

  • You can see these effects with transverse water waves at the seaside as waves hit the protective walls of a harbour BUT you need a very tiny slit to observe diffraction with light waves because of their tiny wavelength.

  • Excluding satellite TV and radio, if it wasn't for diffraction you would never get a radio signal down in a valley - the radio waves bend over the hills!


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WAVE CALCULATIONS - formulae and how to solve problems

  • Be able to use both the equations below, which apply to all waves (and their rearrangements):

    • appropriate units used in ()

    • a) wave speed (metre/second, m/s) = frequency (hertz, Hz) x wavelength (metre, m)

      • in 'shorthand'    v = f x λ

        • rearrangements: 

        • frequency = speed wavelength,   f = v λ 

        • wavelength = speed frequency,   λ = v f

    • b) wave speed (metre/second, m/s) = distance (metre, m) time (second, s)

      • in 'shorthand'    v = d t

        • rearrangements:  d = v x t   and   t = d v

      • This is the general formula for the speed or velocity of anything moving.

    • (a), (b)

    • Note that you are not required to recall the value of the speed of electromagnetic waves through a vacuum ...

      • .. it is very big, 'speed of light' = v = 3 x 108 m/s

      • Be able to do examples of calculations using the wave speed formula and its rearrangements.

    • Wave frequencies are often given in kilohertz or megahertz.

      • 1 kHz   1000 Hz,  1 MHz 1 000 000 Hz, 1 MHz 1000 kHz

    • -

 

Examples of wave calculations

Q1 A wave has a speed of 0.15 m/s and a wavelength of 5.0 cm.

(a) Calculate the frequency of the wave

f = v λ 

5.0 cm 5/100 m = 0.05 m

Therefore frequency = 0.15/0.05 = 3.0 Hz

(b) Calculate the period of the wave.

period = 1 / frequency = 1 / 3 = 0.33 s

 

Q2 The frequency of sound in air at room temperature and pressure is 343 m/s.

The musical note middle C has a frequency of 262 Hz.

Calculate the wavelength of the middle C sound.

λ = v f

wavelength = 343 262 = 1.31 m (131 cm, 3 s.f.)

 

Q3 A set of ocean waves has a frequency of 0.50 Hz.

If the average distance between the crests of the waves is 10 m, what is the average speed of the ocean waves?

 v = f x λ

speed (m/s) = frequency (Hz) x wavelength (m)

speed = 0.5 x 10 = 5.0 m/s

 

Q4


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EXPERIMENTS WITH WATER WAVES in a ripple tank

Introduction - common points for all three wave experiments described

The apparatus consists of:

A transparent tank of water - so you can clearly observe the waves.

A paddle is suspended over and into the water of the ripple tank.

An oscillating paddle driven by a small electric motor that is slightly off-set from symmetrical rotation - this gives the 'to and fro' rocking action of the paddle.

A variable power supply allows you to vary the rate of 'to and fro' oscillation of the paddle that produces the water waves - this allows a fixed wave frequency to be created AND the ability to vary the water wave frequency. You might even have a 'sophisticated' frequency generator to work the humble paddle!

A stopwatch is essential, plus a small cork, white paper, ruler, pencil, strobe light of variable frequency, graph paper stuck on card and ???

(Note: My diagrams are simplified and don't show the full detail of a good quality ripple tank set-up - could anybody send me a good image of a really good set-up? properly acknowledged of course.)


(a) How to measure the frequency of a wave

(c) doc bHere you place a small cork on the water and start the wave generator.

Choose a start point e.g. the top of a bob, start the stopwatch and time 10 complete oscillations or 'bobs'.

Divide the time by 10 gives you a good average time for one period. Then, a simple calculation ...

Frequency = 1 / period = ? Hz.

You can of course do the calculation directly: Frequency (Hz) = 10 / total time (s)

Repeat with different frequencies.


(b) How to measure the wavelength of a wave

For this experiment you need a graph card at the back of the tank.

Set the oscillator going to give a steady stream of water waves.

Direct the strobe light onto the ripple tank so several of the waves are illuminated.

Adjust the frequency of the strobe light until the waves seem to stand still.

At this point you can then measure the length of e.g. 10 waves against the back projection of the graph card.

Just divide the total length by the number of waves to get an average wavelength in cm ==> m.

You can repeat with different frequencies of the oscillating paddle.

 

See also SOUND - how to measure the wavelength of sound wave

 


(c) How to measure the speed of a wave

(c) doc bYou need two students for this 3rd experiment.

Place a large piece of white paper by the side of the tank.

Place a ruler on the paper alongside the tank.

Start the waves going and track the path of a crest on the paper with the pencil.

The second student starts the stopwatch as the first person starts the tracking.

Therefore you have time and distance data to calculate the speed of the waves.

speed (m/s) = distance (m) / time (s)

If the distance was measured in cm, divide by 100 to get metres.

 


  • Check out your practical work you did or teacher demonstrations you observed, all of this is part of good revision for your end of course examination context questions and helps with 'how science works'.

    • using a class set of skipping ropes to investigate frequency and wavelength,

    • demonstrating transverse and longitudinal waves with a slinky spring,

    • carrying out investigations using ripple tanks, including the relationship between depth of water and speed of wave,


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