IB+DP+Topic+4+WAVES

media type="youtube" key="wYoxOJDrZzw" width="504" height="283" Singing plates - Standing Waves on Chladni plates by physicsgirl from youtube.com published on 28 Apr. 2014

4.1 Oscillations // ** Nature of science: ** // Models: Oscillations play a great part in our lives, from the tides to the motion of the swinging pendulum that once governed our perception of time. General principles govern this area of physics, from water waves in the deep ocean or the oscillations of a car suspension system. This introduction to the topic reminds us that not all oscillations are isochronous. However, the simple harmonic oscillator is of great importance to physicists because all periodic oscillations can be described through the mathematics of simple harmonic motion. (1.10)

//** Understandings: **// • Simple harmonic oscillations • Time period, frequency, amplitude, displacement and phase difference • Conditions for simple harmonic motion

//** Applications and skills: **// • Qualitatively describing the energy changes taking place during one cycle of an oscillation • Sketching and interpreting graphs of simple harmonic motion examples

//** Guidance: **// •Graphs describing simple harmonic motion should include displacement– time, velocity–time, acceleration–time and acceleration–displacement •Students are expected to understand the significance of the negative sign in the relationship: a ∝ - x


 * Aims: **

• Aim 6: experiments could include (but are not limited to): mass on a spring; simple pendulum; motion on a curved air track

• Aim 7: IT skills can be used to model the simple harmonic motion defining equation; this gives valuable insight into the meaning of the equation itself

**//Data booklet reference://** T = 1///f//

Simple Harmonic Motion: A fundamental __ oscillation __ that appears in various natural phenomena. When a __force__ acting on a body is __proportional to the displacement__ of the body from some equilibrium position, a repetitive back and forth motion occurs about this position and this __force__ is always __directed toward the equilibrium__ position. It is a periodic motion that is called vibration, harmonic motion and also oscillation, or simple harmonic motion. An object oscillates such that its position is specified by a sinusoidal function of time with no loss in mechanical energy. In real mechanical systems, damping (loss of energy/effects of frictional forces) are often present. [|Simple Harmonic Motion] from University of Salford MANCHESTER DISPLACEMENT: The distance of a particle in the wave from the rest position. AMPLITUDE: The maximum displacement of a particle.  TIME PERIOD (T): The time taken for one oscillation. FREQUENCY (f): The number of oscillations in one second.

= CREATING WAVE DIAGRAMS = media type="custom" key="28912938"

Plot a displacement-distance graph. Below is an example using Word, but you can do this with any program and method which suits you (Excel, Keynote etc.)
 * A) DISPLACEMENT-DISTANCE GRAPH **
 * 1) Open the Waves on a String simulation.
 * 2) Create a wave with Tension = high; Damping = zero; 'No end'; 'Oscillate'.
 * 3) Take a screenshot and paste it into your notes.
 * 4) Use two-ended arrows to label two different positions on the wave indicating Amplitude and Wavelength.
 * 5) Add two axes for Displacement (vertical axis) and Distance (horizontal axis).

Define period What is a wave? There are many different types of waves that propagate through space or a medium. Most of waves, we are unable to see and require a medium to transmit energy. This lesson you will use slinkys in order to observe the properties of the two different types of waves (Longitudinal and transverse).
 * B) DISPLACEMENT-TIME GRAPH : Plot a displacement-time graph. **
 * 1) Use the previous settings, but change the amplitude to 100. Keep frequency = 50
 * 2) Place a vertical ruler as shown so that displacements of the green ball above and below the dotted line can be measured. (Make sure you always measure the position of the same point on the ball each time.)
 * 3) Set the timer to zero and then step the wave through one full oscillation.
 * 4) Record displacement/ cm against time/ s in a spreadsheet.
 * 5) Plot the displacement-time graph for the green ball.
 * 6) Label the graph with Time Period and Amplitude (see example below).
 * Displacement/ cm || Time/ s ||
 * 24.8 || 0.00 ||

Task: In groups of three or four, make a short MOVIE reflecting the lesson objectives below. Upload your videoclip or share the link of your movie. You will use a slinky in order to simulate wave energy and measure the results using different measuring techniques. Save your research reflecting the objectives below and upload the document before the end of the class.

Objectives: 1. Produce and observe the different types of waves through the medium of a slinky and be able to identify them. 2. Observe how the same wave propagates differently depending on the medium and be able to articulate the cause for the changes.

Questions to help address objective 1. a. Using your longitudinal wave that your group produced, find the wavelength, frequency and then calculate the velocity of the wave. b. Can we change the velocity of a wave produdced in your slinky? Compare two transverse waves and calculate the velocity of each wave. (Evidence needed: screen shots of your waves. ) c. Compare and contrast "Transverse and Longitudinal waves".

** Simple Harmonic Motion ** (SHM) A mass on a frictionless surface that is attached to a spring. When the block is disturbed from its equilibrium position, it will oscillate naturally without being driven by some external source of energy. Ignoring any frictional effects or damping, the mass attached to spring will vibrate back-and-forth with a single frequency.  Image from [|www.physics.usyd.edu.au]

The restoring force acting on the mass always is directed back to the equilibrium position.

F ** α ** -x a ** α **-x (as F = ma )

<span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">When the block reaches the equilibrium position it will be moving with its maximum velocity. Total energy //E// = PE + KE = constant <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;"> The mechanical energy of the mass-spring system is conserved.

[|Mass on a spring] applet [|Waves app] simulations, <span style="font-family: &#39;Times New Roman&#39;; font-size: medium;">[|Link to the PhysicsWaves app] on iTunes

<span style="background-color: #ffffff; font-family: &#39;Times New Roman&#39;; font-size: medium;">Wave graphs:[| Displacement - Time, Velocity - Time, Acceleration - Time] from johnvagabondscience.wordpress.com

4.2 Travelling waves //**Nature of science:**// Patterns, trends and discrepancies: Scientists have discovered common features of wave motion through careful observations of the natural world, looking for patterns, trends and discrepancies and asking further questions based on these findings. (3.1)

//** Understandings: **// • Travelling waves • Wavelength, frequency, period and wave speed • Transverse and longitudinal waves • The nature of electromagnetic waves • The nature of sound waves

//** Applications and skills: **// • Explaining the motion of particles of a medium when a wave passes through it for both transverse and longitudinal cases • Sketching and interpreting displacement–distance graphs and displacement– time graphs for transverse and longitudinal waves • Solving problems involving wave speed, frequency and wavelength • Investigating the speed of sound experimentally

//** Guidance: **// • Students will be expected to derive c = f λ • Students should be aware of the order of magnitude of the wavelengths of radio, microwave, infra-red, visible, ultraviolet, X-ray and gamma rays

• c = fλ
 * Data booklet reference: **

WAVELENGTH (λ): The distance along the wave from one particle to the next particle making an identical oscillation.

LONGITUDINAL WAVE: Wave where the oscillation is parallel to the direction in which the energy travels.
 * [[image:nothingnerdy/Long_wave.gif]] || [[image:Longitudinal wave centre of compression.PNG width="450" height="131"]] ||
 * Animation courtesy of Dr. Dan Russell, Kettering University || Compression in longitudinal image from Pearson Baccalaureate by Chris Hamper ||

TRANSVERSE WAVES: Wave where the oscillation is perpendicular to the direction in which the energy travels
 * [[image:nothingnerdy/Trans_wave.gif]] ||
 * Animation courtesy of Dr. Dan Russell, Kettering University ||

Displacement - distance and Displacement - time graphs worksheet



[|Waves applet] from falstad.com [|Various Waves] from www.acs.psu.edu/drussell/demos.html WAVESPEED: The speed with which the energy of the wave travels. v = f × λ







[|EM Spectrum] from Libretexts


 * ELECTROMAGNETIC SPECTRUM / EM spectrum ** :

Light is an electromagnetic wave; that is a propagation of transverse disturbance in an electric and magnetic field. The range of electromagnetic waves ordered by frequency and wavelength including light, heat, radio, gamma rays, microwaves, X-rays The wavelength of visible light can vary from 400nm to 800nm. It consists of varing magnetic and electric field and displays wave phenomena including reflection, refraction, differaction and interference.
 * EM waves can travel through a vacuum. **** The speed of EM waves in a vacuum is c = 3 x 10 8 ms -1 . **

WHAT IS AN EM WAVE? APPLET [|LINK TO NASA WEBSITE ABOUT EM SPECTRUM]
 * media type="youtube" key="jnGTCaiZqOE" width="560" height="315" || media type="youtube" key="BUYeQa_-ojk" width="560" height="315" ||
 * [|Limits of Light] - The Secrets of Nature <span style="color: #111111; font-family: Roboto,Arial,sans-serif; font-size: 10px;">[|The Secrets of Nature] <span style="font-family: Roboto,Arial,sans-serif; font-size: 10px;">Published on 2 May 2014 || [|What is Light] - Physics (Simple Explanation) <span class="view-count style-scope yt-view-count-renderer" style="color: var(--yt-metadata-color);"><span style="font-family: Roboto,Arial,sans-serif; font-size: 10px;">[|The Real Physics] Published on 4 May 2017 ||

4.3 Wave characteristics //** Nature of science: **// Imagination: It is speculated that polarization had been utilized by the Vikings through their use of Iceland Spar over 1300 years ago for navigation (prior to the introduction of the magnetic compass). Scientists across Europe in the 17th–19th centuries continued to contribute to wave theory by building on the theories and models proposed as our understanding developed. (1.4)

//** Understandings: **// • Wavefronts and rays • Amplitude and intensity • Superposition • Polarization

//** Applications and skills: **// • Sketching and interpreting diagrams involving wavefronts and rays • Solving problems involving amplitude, intensity and the inverse square law • Sketching and interpreting the superposition of pulses and waves • Describing methods of polarization • Sketching and interpreting diagrams illustrating polarized, reflected and transmitted beams • Solving problems involving

//** Malus’s law Guidance: **// • Students will be expected to calculate the resultant of two waves or pulses both graphically and algebraically • Methods of polarization will be restricted to the use of polarizing filters and reflection from a non-metallic plane surface

//** Data booklet reference: **// • I ∝ A 2 • I ∝ x −2 • I = I 0 cos 2 θ

A wavefront is a line of surface which joins all points which (have the same displacement at the same moment. They) are all in phase. A ray is an arrow representing the path taken by the wave energy as it travels away from a source. Intensity is a measure of the amount of energy a wave brings to a unit area every second. The intensity of a wave depends on its amplitude. larger amplitude = larger intensity It has been found that a wave's intensity is proportional to the square of the amplitude. (Inverse square law) I ∝ A 2 The light intensity diminishes the further it travels. This is due to the energy (intensity) of the light dissipating ( means ‘spreading out’ ) in a spherical manner. Therfore, the intensity of the received radiation is inversely proportional to the square of the distance from the point source to the receiver: I ∝ x -2
 * media type="youtube" key="9Q4xxRPduYw" width="560" height="315" || media type="youtube" key="0t5GHR6opfI" width="560" height="315" || media type="youtube" key="r-9uMxmj-HQ" width="560" height="315" ||
 * Maui Jim Polarised Sunglasses; A commercial from youtube.com || <span style="background-image: url(">[|Polarised vs Non-Polarised sunglasses for flying] from youtube.com || [|The effects of polarised sunlgasses] on smatphones from youtube.com ||

Virtual Physics - [|Polariser]
 * media type="youtube" key="gP751qpm4n4" width="560" height="315" || media type="youtube" key="8YkfEft4p-w" width="560" height="315" || media type="youtube" key="KM2TkM0hzW8" width="560" height="315" ||
 * <span style="background-image: url(">[|Polarised light] by Kevin Claytor published on 9 Nov 2013 youtube.com || <span style="background-image: url(">[|Polarisation of Ligh] t: cirdularly polarised, linearly polarised, uppolarised light by Eugene Khutoryansky published on 12 Nov. 2015 youtube.com || Polarisation by sixty symbols uploaded on 13 Aug 2009 from youtube.com ||

** Polarisation **
When light passes through polaroid, it becomes polarised in one direction. Visible light from the Sun is unpolarised light in which an electric field and a magnetic field at right angles to each other propagate along a direction that is normal to both field. <span style="font-family: Calibri,sans-serif; font-size: 11pt;">In unpolarised light the electric field vector may vibrate in any plane (normal/perpendicular to the direction of propagation) while in polarised light the electric field vibrates in one plane only. T he direction of polarization of an [|Polarised light simulation] from doitpoms.ac.uk
 * [[image:sciencelanguagegallery/polarizationfigure1.jpg]] ||  || [[image:Plane of polarised light.PNG width="699" height="248"]] ||

electromagnetic wave to be the direction of the electric-field vector E ; not the magnetic field B (Plane polarised:the electric field oscillates on the same plane. The plane formed by E and the direction of propagation is called the plane of polarizationof the wave.)

Malus' law
The intensity of the light is proportional to the square of the amplitude. I = I 0 cos 2 θ I 0 = Initial intensity of incident light in Wm -2 I = Intensity of transmitted light in Wm -2 θ = angle between transmitted ray and an analyser (polarisers) in o.

If a beam of light passes through a narrow slit (close to the wavelength of light around 500nm), it will diffract(spread out). Waves only interfere if they have the same frequency and similar amplitude.
 * Light reflects and refracts, and then it also interferes and diffracts **.

The amplitude of light is related to its brightness. ** The intensity of light is proportional to the square of the amplitude. **

EXAMPLE: Sketch a graph to show how the intensity I of the transmitted light varies with <span style="font-family: Symbol,sans-serif;"> q as the analyser is rotated through 2 <span style="font-family: Symbol,sans-serif;">p. SOLUTION: Graph of Intensity vs angular position I = I 0 cos 2 θ || || PRACTICE: Place one more analyser (polariser 3, Refer to figure 1 above) behind polariser2. Sketch a graph to show how the intensity of the transmitted light varies with <span style="font-family: Symbol,sans-serif;"> q as the analyser is rotated through <span style="font-family: Symbol,sans-serif;">p/2. SOLUTION:
 * [[image:malus.PNG width="521" height="259"]]
 * Image from [|www.researchgate.net] || Image of cos 2 θ graph from [|www.evidyarthi.in] ||

PRACTICE( Worked example 4.11 taken from text K.A.Tsokos): Vertically polarised light of intensity Io is incident on a polariser that has its transmission axis at <span style="font-family: Symbol,sans-serif; font-size: 13px;">q 30 o to the vertical. The transmitted light is then incident on a second polariser whose axis is at <span style="font-family: Symbol,sans-serif; font-size: 13px;">q 60 o to the vertical. Calculate the factor by which the transmitted intensity is reduced. SOLUTION: After passing through the first polariser the intensity of light is I = I o cos 2 θ = I o cos 2 30 o = (3/4) I o The second polariser has its transmission axis at θ = 30 to the first polariser, and so the final transmitted light has intensity I 2nd = (3/4) I o cos 2 θ = (3/4) I o cos 2 30 = 9/16 I o The intensity is thus reduced by __ a fator of 9/16 __ PRACTICE(Question taken from text K.A.Tsokos): Two polarisers have their transmission axes at right angles to each other. A third polariser is inserted in between the first two. Its transmission axis is at 45o to the other two. Determine whether any light will be transmitted by this arrangement of three polarisers. SOLUTION: The intensity of transmitted light is equal to the magnitude of (1/8) I o

Malus' law

Interference
Eg) Water (ripple tank) Sound (speakers) Light (Soap Bubbles)
 * [[image:pulses.gif width="436" height="171"]] || [[image:constructive and destructive interference.gif width="423" height="170"]] ||
 * [|Superposition of two opposite direction wave pulses] from Penn State University || [|Constructive and destructive interference] from Penn State University ||
 * Superposition** is the phenomena when two or more waves interfere with each other.

There are two types of interference: 1) **Constructive** (in phase) interference occurs when 2 corresponding maximums (crests) OR minimums (troughs) interfere creating a supercrest OR supertrough. 2) **Destructive** (out of phase) interference occurs when maximum (crest) interferes with a minimum (troughs) which cancel out to create no wave at all. Two oscillations are completely out of phase when the graphs are displaced by an angle π. The' Phase Difference' is π.

4.4 Wave behaviour //** Nature of science: **// Competing theories: The conflicting work of Huygens and Newton on their theories of light and the related debate between Fresnel, Arago and Poisson are demonstrations of two theories that were valid yet flawed and incomplete. This is an historical example of the progress of science that led to the acceptance of the duality of the nature of light. (1.9)

//** Understandings: **// • Reflection and refraction • Snell’s law, critical angle and total internal reflection • Diffraction through a single-slit and around objects • Interference patterns • Double-slit interference • Path difference

//** Applications and skills: **// • Sketching and interpreting incident, reflected and transmitted waves at boundaries between media • Solving problems involving reflection at a plane interface • Solving problems involving Snell’s law, critical angle and total internal reflection • Determining refractive index experimentally • Qualitatively describing the diffraction pattern formed when plane waves are incident normally on a single-slit • Quantitatively describing double-slit interference intensity patterns

//** Guidance: **// • Quantitative descriptions of refractive index are limited to light rays passing between two or more transparent media. If more than two media, only parallel interfaces will be considered • Students will not be expected to derive the double-slit equation • Students should have the opportunity to observe diffraction and interference patterns arising from more than one type of wave

//** Data booklet reference: **// • //n// 1 ///n// 2 = sin θ 2 / sin θ 1 = v 2 /v 1 • s = λD/d • Constructive interference: path difference = n λ • Destructive interference: path difference = (n+1/2) λ

Ray: The straight line in which light travels. A light ray is represented by a __ straight __ line with an __ arrow __ to show the direction of motion. __ R eflection __ : Light bounces off on the surface of an object. __ R efraction __ : Light changes its direction when it passes from one medium to another.

Snell's law: <span style="background-image: url(">[|The laws of refraction with examples] from www.physicstutorials.org Wavefronts are __ perpendicular __ to the ray. || ||  ||
 * sin //i// / sin //r// = //n// **
 * [[image:sciencelanguagegallery/refraction of wavefronts.gif width="319" height="305"]]
 * [|mage from http://electron6.phys.utk.edu] || [|Refraction at a boundary in two media] from AP Physics Class Notes || [|Image from www.astarmathsandphysics.com] ||

=
**[|Refractive index]** : The ratio of the speed of light in a vacuum to its speed in a specified medium. =====

=
The measure of the bending of a ray of light when passing from one medium into another. If //i// is the [|angle of incidence] of a ray in vacuum (angle between the incoming ray and the perpendicular to the surface of a medium, called the normal), and //r// is the [|angle of refraction] (angle between the ray in the medium and the normal), the refractive index //n// is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction; //i.e., n// = sin //i// / sin //r//. Refractive index is also equal to the velocity //c// of light of a given wavelength in empty space divided by its velocity //v// in a substance, or //n// = //c/////v//. =====

PRACTICE Question: 1) A cook found a clear solid determines that light travels at 1.96 x 10 8 m/s through the material. Should the cook take the solid to a jeweler, or should she use it for dinner?

2) If you found a refractive index of unknown crystal as less than 1, will it make you a famous scientist?

SNELL'S LAW from Youtube.com media type="file" key="Refraction Part1.flv.flv" width="390" height="390"
 * Snell’s law **

Go to S-Cool Wave properties websites

[|Lab report] (20%)

Interference pattern
[|Interference patterns of two point sources image] from fphoto.photoshelter.com Summary of interference patterns, image from roncalliphysics.wikispaces.com || Constructive interference where the path difference is n λ || Destructive interference where the path difference is (n + ½) λ ||
 * [[image:Summary of the path difference.PNG width="511" height="273"]]
 * [[image:Path difference of n.PNG width="516" height="291"]]
 * [[image:Path difference of half n.PNG width="513" height="287"]]

Path difference
Constructive interference occurs when there is zero phase difference: path difference = nλ Destructive interference occurs when there is a ‘half cycle/180 degree/π radians’ phase difference: path difference = (n + ½)λ n = number of wavelengths from central maximum (0, 1, 2, 3…) λ = wavelength (m)

//__Worked example 4.14 K.A. Tsokos text__// Identical waves leaving two sources arrive at point P. Point P is 12m from the first source and 16.5m from the second. The waves from both sources have a wavelength of 3m. State and explain what is observed at P. Answer) The path difference is 4.5 metres. Dividing by the wavelength, the path difference is equal to (1+1/2)3m. It is a half-integral multiple of the wavelength. We thus have destructive interference.

Double slits interference
2 Sep 2013 from youtube ||
 * media type="youtube" key="kKdaRJ3vAmA" width="560" height="315" ||
 * <span style="background-image: url(">[|How To Make Your Own Double Slit Experiment (Young's)] byTechLaboratories

Double slits interference intensity pattern
s = λD / d = ( 675 x 10 -9 x 4.50 ) / ( 1.25 x10 -3 ) = 0.00243 m. λ = //__2.43 mm__// || PRACTICE: Two slits are 0.1 mm apart. Determine the distance from the central maximum to the next maximum if the light has wavelength 530 nm and the screen is 2m away. What is the distance from central max to first dark ? SOLUTION: s = 530 nm x 2 m /10 -4 m = 1.06 cm First dark appears when d sin theta is equal to half of the wavelength. So the distance central max to first dark is 0.53 cm PRACTICE: Distance between bright bands is 0.7 cm when d = 0.2 mm and D = 3 m. What is the wavelength ? SOLUTION: Bright band appears when n = 1 λ = ds/D = (7 x 10 -3 x 2 x 10 -4 )/ 3m = 467 nm //__**Worked example** 4.15 from K.A.Tsokos text__// In a double-slit interference experiment, the two slits are separated by a distance of 4.2 x 10 -4 m and the screen is 3.8m from the slits. Using figures above, a. Determine the wavelength of light used in this experiment. ( Hint: λ = ? m, D = 3.8 m, and d = 4.2 x 10 -4 m, s = 0.50 x 10 -2 m ) λ = ds / D = 5.5 x 10 -7 m b. Suggest the effect on the separation of the fringes of decreasing the wavelength of light. From the formula, we see that if we decrease the wavelength the separation __ decreases __. c. State the feature of the graph that enables you to deduce that the slit width is negligible. The intensity of the side fringes is__** equal to **__ the intensity of the central fringe. media type="youtube" key="kO2yFC7_k2s" width="560" height="315" MIT Physics Demo -- Microwave Interference <span style="font-family: Roboto,Arial,sans-serif; font-size: 10px; text-decoration: none;">[|mittechtv] Uploaded on 12 May 2008 <span style="background-color: #ffffff; color: #555555; font-family: &#39;Helvetica Neue&#39;,Helvetica,Arial,sans-serif; font-size: 12px;">Tsunami propagation 2011 japan ||
 * [[image:sciencelanguagegallery/Light interference pattern.PNG width="340" height="290"]] || [[image:Double slits interference pattern.PNG width="640" height="271"]] ||
 * Young's double slit interference pattern || [|Image from iss.schoolwires.com]
 * [[image:Intensity pattern for double slits.JPG width="304" height="470"]] || [[image:Double slits interference pattern.JPG width="309" height="473"]] ||
 * Graphs showing the level of Intensity for double slits || Interference pattern for double slits ||
 * [[image:nothingnerdy/tsunami_propagation_2011_japan.jpg]] ||
 * The energy of the wave spreads out around obstacles and through gaps

**Wave phenomena** DIFFRACTION APPLET DIFFRACTION: The way waves can spread out after passing an object or opening with a size similar to the wavelength of the wave. media type="youtube" key="BH0NfVUTWG4" width="560" height="315" Apertures and Diffraction - Exploring Wave Motion (3/5) <span style="font-family: Roboto,Arial,sans-serif; font-size: 10px;">[|ouLearn on YouTube] Uploaded on 26 Jul 2011
 * [[image:nothingnerdy/diffraction.jpg]] ||
 * More diffraction through a narrow gap ||

Waves pass through the 'slit' created by the land forms. The waves coming around Island interfere with the other waves, creating an interference pattern.
 * Fun Winter Break Research Activity : Christmas Present for AIS Year12 2016: **
 * IN THE SITUATIONS BELOW, COMMENT ON THE TYPE OF WAVES, THE WAVELENGTH, AND PHENOMENA OR THE RELATIONSHIP BETWEEN THE WAVELENTH AND THE SIZE OF THE GAP **
 * [[image:nothingnerdy/diffraction_electrons.jpg width="322" height="286"]] || [[image:diffraction_photoelectrons simulated.jpg width="800" height="238"]]

Simulated <span style="background-image: url(">[|photoelectron diffraction pattern] Image from www.researchgate.net || Images; diffraction of light from [|physics to go]. Diffraction from www.britannica.com/science/diffraction RIPPLE TANK SIMULATION WITH MANY OPTIONS
 * [|Diffraction of electrons] Image from www.bristol.ac.uk || [|High energy photoelectron diffraction] from IOPSCIENCE : <span style="color: #000000; font-family: franklin-gothic-urw-cond,sans-serif; font-size: 24px; text-decoration: none; vertical-align: baseline;">[[image:http://cms.iopscience.iop.org/alfresco/download/direct/workspace/SpacesStore/94f97534-d09c-11e5-b0b6-759f86a2008e/njp-2016.png?guest=true width="152" height="12" link="http://iopscience.iop.org/journal/1367-2630"]] ||



4.5 Standing waves Common reasoning process: From the time of Pythagoras onwards the connections between the formation of standing waves on strings and in pipes have been modelled mathematically and linked to the observations of the oscillating systems. In the case of sound in air and light, the system can be visualized in order to recognize the underlying processes occurring in the standing waves. (1.6)
 * // Nature of science: //**

//** Understandings: **// • The nature of standing waves • Boundary conditions • Nodes and antinodes

//** Applications and skills: **// • Describing the nature and formation of standing waves in terms of superposition • Distinguishing between standing and travelling waves • Observing, sketching and interpreting standing wave patterns in strings and pipes • Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave

//** Guidance: **// • Students will be expected to consider the formation of standing waves from the superposition of no more than two waves • Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries • Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries • For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes • The lowest frequency mode of a standing wave is known as the first harmonic • The terms fundamental and overtone will not be used in examination questions

**The principle of superposition** - The net displacement of the medium / particles (through which waves travel) due to the superposition is equal to the sum of individual displacements (produced by each wave).


 * Superposition of Waves ** The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any point in space or time, is simply the sum of the individual wave dispacements. This is true of waves which are finite in length (wave pulses) or which are continuous sine waves.

Animation of superposition and standing waves

**Standing waves** - The wave profile doesn’t progress. Standing (stationary) waves are the result of the superposition of two waves (with the same speed, frequency and amplitude) travelling in opposite directions.

The periodic disturbance in a medium resulting from the combination of two waves of equal frequency and intensity travelling in opposite directions. All points in between two nodes on a standing wave are in phase. (whereas points on a progressive wave that are closer than one wavelength are all out of phase.) The phase difference is represented by an angle (usually in radians).

Node: A place on the wave that doesn’t move at all where the displacement is zero. Antinode: A place on the wave where the amplitude is the maximum.

Standing waves applet [|Standing waves animations] from www.animations.physics.unsw.edu.au

**Stringed instruments**
Harmonics on a string


 * [[image:sciencelanguagegallery/images.jpg width="338" height="359"]] || [[image:Modes on a string UNSW.PNG width="1043" height="357"]] ||
 * || [|Images from School of Physics UNSW] www.animations.physics.unsw.edu ||

Experiment idea on<span style="background-image: url(">[| Wave velocity and Tension] from INTHINKING IB PHYSICS The speed of a wave in a string. // T= // the tension, μ= The mass per unit length Therefore, the wave in the thicker strings is slower than in the thin strings and //f// = v / λ This is why a thick guitar string is a lower note than a thin one and why the note gets higher when you increase the tension.

From diagrams below, each of the possible waves is called a harmonic. The first harmonic(the fundamental frequency) is the wave with the lowest possible frequency. Harmonic motion, as of a violin string, can be analyzed as the sum of harmonic frequencies or harmonics, each of which is itself a kind of harmonic motion. All the possible standing waves are produced. media type="youtube" key="0rbJ0yNjkqo" width="560" height="315" [|Standing Wave 3 - Both Ends Fixed] by [|Christopher]

**Standing waves in closed pipes.**
When a standing wave is formed in a closed pipe, only ** odd harmonics ** are formed.



**Standing waves in open pipes.**
When a standing wave is formed in a open pipe, ** all the harmonics ** are formed. media type="youtube" key="o7Sz7B0VYAs" width="560" height="315" Standing waves in long spring open end by [|PhysicsExperiments.org] Images from Pearson IB Higher Level Physics Chris Hamper || || media type="youtube" key="QotfmiDDzLw" width="560" height="315" [|Standing Wave 4] - Both Ends Free by [|Christopher]
 * [[image:standing waves in air columns ONE open end pipes.PNG]]
 * Standing waves in air columns: One open end || Standing waves in air columns: Both open ends ||

Image from [|Standing Waves (Acoustic resonance)]

Wikipedia - [|harmonics on guitar string] [|Standing waves in pipes] from www.s-cool.co.uk [|Standing waves practice questions] from IB InThinking [|Standing waves on a string] Stanford University

**Examples** ( Consider the speed of sound in air as 340m/s )
Answer 1. Pipes: The fundamental frequency of a pipe closed at one end is // f //. A pipe of the same length but open at both ends has a fundamental frequency (first harmonic) of A.(1/2) // f // B. // f // C. 2 // f // D.4 // f //

Answer 2. Organ pipes: What will be the fundamental frequency and first three overtones for a 26 cm long organ pipe if it is (a) open (b) closed

Answer <span class="wiki_link_new" style="background-color: #ffffff;">3. Flute: A flute is designed to play middle C (262Hz) as the fundamental frequency when all the holes are covered. Approximately how long should the distance be from the mouthpiece to the far end of the flute?

<span class="wiki_link_new" style="background-color: #ffffff;">Answer 4. Wind noise frequencies: Wind can be noisy - it can "moan" in chimneys ( length:3m ). What is causing the noise, and about what frequency would you expect to hear?

from 2007 to 2005 - some questions on standing waves [|Standing waves worksheets] from TuHSPhysics [|IB Physics Standing waves problem] from fcis.aisdhaka.org PHET WAVE ON A STRING SIMULATION

** IB Practice Questions: **
[|Standing waves worksheet and solutions] from sites.google.com/a/ttsd.k12.or.us/tuhsphysics/home/htp-physics-g/wavesandsound/standingwavesworksheet



Recall the Characteristics of Waves from IGCSE
Light Sound Refraction Diffraction [|More Waves practice questions] from pstcc.edu [|AP PHYSICS CLASS NOTES] Read and solve questions at [|Resonance and standing waves] from gbhsweb.glenbrook225.org
 * Resonance: <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">The increase <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> in <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">amplitude <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> of <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">oscillation <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> of an <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">electric <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> or <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">mechanical system exposed <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> to a <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">periodic force whose frequency <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> is <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">equal <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> or <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">very close <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> to <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">the natural undamped frequency <span style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;"> of <span class="hvr" style="background-color: #ffffff; color: #404040; font-family: Arial,Helvetica,sans-serif;">the system.
 * media type="youtube" key="iyw4AcZuj5k" width="560" height="315" || media type="youtube" key="P0k02IXiVUQ" width="560" height="315" ||
 * [|Resonance]: A Perfect Experiment [|scienceforall] by [|perihelion.gr] Published on 10 Nov 2012 || [|Oil Rig Engineering Connections] - BBC Documentary Published on 13 May 2013 ||