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AS Physics Unit 12 Waves AS Physics Unit 12 Waves Mr D Powell.

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Presentation on theme: "AS Physics Unit 12 Waves AS Physics Unit 12 Waves Mr D Powell."— Presentation transcript:

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2 AS Physics Unit 12 Waves AS Physics Unit 12 Waves Mr D Powell

3 Mr Powell 2011 Index Chapter Map Dont be confused by the necessarily transverse depiction of (longitudinal) sound waves on an oscilloscope. Differentiating between wavelength and time period is very important here. Also remember your units.

4 Mr Powell 2011 Index 12.1 Waves and vibrations Specification link-up 3.2.3: Progressive waves; Longitudinal and transverse waves 1.What are the differences between transverse and longitudinal waves? 2.What is a plane-polarised wave? 3.What physical test can distinguish transverse waves from longitudinal waves? Specification link-up 3.2.3: Progressive waves; Longitudinal and transverse waves 1.What are the differences between transverse and longitudinal waves? 2.What is a plane-polarised wave? 3.What physical test can distinguish transverse waves from longitudinal waves?

5 Mr Powell 2011 Index Longitudinal Waves

6 Mr Powell 2011 Index Longitudinal © John Parkinson 5 The direction of vibration of the particles is parallel to the direction in which the wave travels. Common examples:-Sound, slinky springs seismic p waves Longitudinal waves cannot be polarised Direction of travel VIBRATION

7 Mr Powell 2011 Index Transverse © John Parkinson 6 The direction of vibration of the particles is perpendicular to the direction in which the wave travels. Common examples:- Water, electromagnetic, ropes, seismic s waves You can prove that you have a transverse wave if you can polarise the wave (especially important with light (electromagnetic) as you cannot see the wave!!) Direction of travel vibration

8 Mr Powell 2011 Index Polarisation

9 Mr Powell 2011 Index Uses of Polarisation

10 Mr Powell 2011 Index Fishing?

11 Mr Powell 2011 Index Using polarisation to measure concentration © John Parkinson 10 Sugar solution laser polariser analyser 1.Some liquids are optically active and rotate the electric vector. 2.The liquids concentration is proportional to the electric vector rotation.

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13 Mr Powell 2011 Index Stress Analysis © John Parkinson 12 The structure of certain plastics will show polarisation. When viewed under stress the structure polarises the light differently. The place where stress is greatest shows a more rapid colour change. Models can be made of complex components which are viewed with a polarising filter so engineers can design out the stresses.

14 Mr Powell 2011 Index LCD Displays © John Parkinson 13

15 Mr Powell 2011 Index Summary Questions © John Parkinson 14

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18 Mr Powell 2011 Index 12.2 Measuring waves Specification link-up 3.2.3: Progressive waves; Longitudinal and transverse waves 1.What is meant by the amplitude of a wave? 2.Between which two points can the wavelength be measured? 3.How is the frequency of a wave calculated from its period? Specification link-up 3.2.3: Progressive waves; Longitudinal and transverse waves 1.What is meant by the amplitude of a wave? 2.Between which two points can the wavelength be measured? 3.How is the frequency of a wave calculated from its period?

19 Mr Powell 2011 Index What is missing?

20 Mr Powell 2011 Index Key Terms…

21 Mr Powell 2011 Index Practical - Measure the Speed of Sound Each student or group of students will require the following equipment: 1.some sticky-tac or tape 2.a dual-beam oscilloscope (or a single-beam oscilloscope with an x-input) 3.a signal generator 4.a loudspeaker (or hum into a mic) 5.a microphone on a stand 6.connecting wires 7.a metre ruler Aims In this experiment you will measure the speed of sound using a loudspeaker, a microphone and an oscilloscope. This will provide you with further experience of using an oscilloscope to observe wave patterns.

22 Mr Powell 2011 Index Example Results... Output Frequency 6000Hz StartwavelengthFreqSpeed 0.03--- 0.0820.0526000312 0.140.0586000348 0.1950.0556000330 0.2540.0596000354 0.30.0466000276 Ave0.054324 Look at your results of the example results and think about the errors in your exp? The percentage uncertainty in the speed of sound is equal to the sum of the percentage uncertainties in the measurement of frequency and wavelength. Note that measuring more than one wavelength minimises the uncertainty in the measurement. For example, measuring two wavelengths halves the measurement uncertainty and measuring three reduces it to a third. The speed of sound increases if the temperature of the air increases. How do you think an increase of the air temperature would affect your measurements?

23 Mr Powell 2011 Index Q. A mains transformer vibrates the floor at 50Hz. What is the time for a complete cycle? 360 o = 2 radians Timings?

24 Mr Powell 2011 Index speed = distance time Wave Speed Equation

25 Mr Powell 2011 Index Wave Speed Equation

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28 Mr Powell 2011 Index b) ¾ of cycle later Q would be at a trough point and returning to centre

29 Mr Powell 2011 Index 12.3 Wave properties 1 Specification link-up 3.2.3: Refraction at a plane surface; Diffraction 1.What causes waves to refract when they pass across a boundary? 2.In which direction do light waves bend when they travel out of glass and into air? 3.What do we mean by diffraction? Specification link-up 3.2.3: Refraction at a plane surface; Diffraction 1.What causes waves to refract when they pass across a boundary? 2.In which direction do light waves bend when they travel out of glass and into air? 3.What do we mean by diffraction?

30 Mr Powell 2011 Index Virtual Ripple Tanks… Use the virtual ripple tank here to explore wave properties. http://www.falstad.com/ripple/ Use the ideas from the book on page 179 and also you can download the additional information sheet on the blog to help you explore the ideas. Make summary notes on what you find for each situation. You may decide to screenshot out the image to help you. (NB: pick a nice colour scheme)

31 Mr Powell 2011 Index Diffraction in action....

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36 Mr Powell 2011 Index 12.4 Wave properties 2 Specification link-up 3.2.3: Superposition of waves, stationary waves; Interference 1.What features of two waves must combine in order to produce reinforcement? 2.What is the phase difference between two waves if they produce maximum cancellation? 3.Why is total cancellation rarely achieved in practice? Specification link-up 3.2.3: Superposition of waves, stationary waves; Interference 1.What features of two waves must combine in order to produce reinforcement? 2.What is the phase difference between two waves if they produce maximum cancellation? 3.Why is total cancellation rarely achieved in practice?

37 Mr Powell 2011 Index The Trumpet TrumpetChromatic Scale Period msFrequency Hz (Calculated) Frequency Hz BbBb C4250261 BC#C# 277 CD293 C#C# EbEb 311 DE329 EbEb F349 EF#F# 3333370 FG392 F#AbAb 415

38 Mr Powell 2011 Index Checking a Guitars Tuning.... GuitarPeriod ms Frequency Hz (Calculated) Frequency Hz E0.0052519041 A0.0110055 D0.0128373 G0.01258098 StringNoteFrequency 1 (thinnest)G3G3 97.999 Hz 2D3D3 73.416 Hz 3A2A2 55 Hz 4 (thickest)E2E2 41.204 Hz Thick thin

39 Mr Powell 2011 Index Microwave Diffraction...

40 Mr Powell 2011 Index Definitions... A progressive wave is one where the waveform travels, as opposed to a standing wave (or stationary wave) where the waveform is fixed in place. Most familiar waves are usually progressive: light, sound, and water transmit energy along their direction of travel, though it is possible to set up standing waves for each of these. A plucked string fixed at both ends vibrates in a standing wave though the musical sound it generates is a progressive wave. Progressive waves, despite the name, can travel backwards as well as forwards. A standing wave is equivalent to two equal and opposite progressive waves. It can be either a transverse wave or a longitudinal wave, depending on which direction the vibrations go compared to the direction of travel of the wavefront. The wavefront represents the pattern that is moving along. TASK... Use this information to MAP the similarities and differences between progressive & standing waves. You can also refer to your book as well.

41 Mr Powell 2011 Index supercrest The resultant displacement at any point is the sum of the separate displacements due to the two waves Eg: with a slinky coil spring Principal of Superposition

42 Mr Powell 2011 Index Two square waves superposing:

43 Mr Powell 2011 Index A square wave can be made up from several sine waves of higher frequencies Superposition of sine waves: 3*f o Fundamental frequency

44 Mr Powell 2011 Index LONGITUDINAL PULSETRANSVERSE PULSE Phase Changes in Reflection

45 Mr Powell 2011 Index Interference types.... Constructive Destructive

46 Mr Powell 2011 Index Re-inforcement (constructive interference) Cancellation (destructive interference) Coherent sources (of the same frequency and phase relationship) produce a stable interference pattern. Interference Two dippers in a ripple tank can cause circular wavefronts to re-inforce or cancel:

47 Mr Powell 2011 Index Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference Regions of reinforcement

48 Mr Powell 2011 Index Regions of reinforcement Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference

49 Mr Powell 2011 Index Regions of reinforcement Regions of cancellation Experiments with microwaves: a) The intensity of the receiver signal decreases with distance from the transmitter. b) Microwaves are reflected off metal plates – similar to light on a mirror. c) Diffraction occurs at each slit (slit width is of similar magnitude to the wavelength) d) An interference pattern forms with regions of constructive and destructive interference

50 Mr Powell 2011 Index compressions rarefaction Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers

51 Mr Powell 2011 Index compressions rarefaction Regions of reinforcement (LOUD) Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers

52 Mr Powell 2011 Index compressions rarefaction Regions of reinforcement (LOUD) Regions of cancellation (QUIET) Two loud speakers emitting the same note can cause loud and quiet areas in front of the speakers When compressions (or rarefactions) arrive in phase from both speakers, constructive interference occurs, creating a loud region

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58 Mr Powell 2011 Index 12.5 Stationary and progressive waves Specification link-up 3.2.3: Progressive waves; Superposition of waves, stationary waves 1.What is the necessary condition for the formation of a stationary wave? 2.Is a stationary wave formed by superposition? 3.Why are nodes formed in fixed positions? Specification link-up 3.2.3: Progressive waves; Superposition of waves, stationary waves 1.What is the necessary condition for the formation of a stationary wave? 2.Is a stationary wave formed by superposition? 3.Why are nodes formed in fixed positions?

59 Mr Powell 2011 Index Practical Investigation... 1.Take a ruler and investigate the sound wave it creates by twanging it with your fingers. 2.(Take caution not to break it) 3.Think about the relationship between pitch (frequency) and length. 4.Then make a verbal prediction for what might happen with a string or tube? 5.Write three sentences to your conclusions...

60 Mr Powell 2011 Index The Rubens Tube The classic physics experiment involving sound, a tube of propane and fire. Push the tube to 449 Hz then higher frequencies, then some jazz and then some rock. This is real life sound visualization.... Wave examples Progressive or Standing.... Cornstarch is a shear thickening non- Newtonian fluid meaning that it becomes more viscous when it is disturbed. When it's hit repeatedly by something like a speaker cone it forms weird tendrils. The speaker cone was vibrating at 30 Hz. Chladni plate: Fine sand sprinkled on the plate gathers at the nodes. Similar to a wobble card (Rolf Harris) Jelly A large cubic shape shot by a BB gun.

61 Mr Powell 2011 Index How Science Works – Ernst Chladni Ernst Florens Friedrich Chladni (German pronunciation: November 30, 1756 – April 3, 1827) was a German physicist and musician.Germanphysicistmusician His important works include research on vibrating plates and the calculation of the speed of sound for different gases.vibratingspeed of sound One of Chladni's best-known achievements was inventing a technique to show the various modes of vibration on a mechanical surface. Chladni repeated the pioneering experiments of Robert Hooke of Oxford University who, on July 8, 1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a bow along the edge of a plate covered with flour, and saw the nodal patterns emerge.modes of vibrationRobert HookeOxford Universitynodal patternsbow

62 Mr Powell 2011 Index So what is the necessary condition for the formation of a stationary wave? In essence it is simply that we must have a reflected wave of the same frequency which returns in the opposite direction. When we think of a rope fixed on a wall or an elastic band the features are clear with a clear point where you get a node and antinode effect. The amplitude varies from position from zero to +/-A The phase difference between particles (or displacement position +/-x is... 1.Zero between adjacent nodes, or an even number of nodes 2.180 or if two particles are separated by an odd number of nodes

63 Mr Powell 2011 Index Why are nodes formed in fixed positions? Hopefully you can see that as the wave passes through the reflected wave they cancel at certain points only where the phase is matched. This animation really shows it well as the blue/red waves interfere to produce the black wave. Then you can see the nodes where there is no net movement... http://www.antonine- education.co.uk/physics_a2/module_4/topic_5/topic_5.htm

64 Mr Powell 2011 Index Is a stationary wave formed by superposition? Yes it is and you can see by looking at this graphic. The two waves interfere when the meet. 1.They can either constructively add together 2.Destructively cancel 3.Work to some comprises. Look the combined wave trace for each case.... Think about Mr Powells bathtub model

65 Mr Powell 2011 Index Why are nodes formed in fixed positions? Finding the Speed of Sound

66 Mr Powell 2011 Index Speed of Sound Now try out the experiment as shown. You will have have to be very accurate to make sure it works. Use ICT to make the spreadsheet.... Frequency (Hz)Length (m)Wavelength (m)Velocity (ms -1 ) 288.00.2751.100328 304.40.2851.140335 320.00.2501.000320 341.30.2290.916313 271.20.3001.200325 Ave324 343 dry air 20 o C

67 Mr Powell 2011 Index Data Trends... Discuss this data with a partner. Can you see a trend in the numbers? Can you comment on... Gas -> Liquid -> Solid the mass of the molecules or compounds? (as best you know) Ethanol C 2 H 5 OH Chloroform CHCl 3 Glass SiO 2 The bonding or strength of the structures You can use the periodic table to help you?

68 Mr Powell 2011 Index Can you explain this? 1.Imagine you are holding a rope at one end which is attached to a brick wall at the other. 2.You are sending regular oscillations down the rope and something weird is happening. Words to help... Frequency, amplitude, phase, node, antinode, super crest, super trough, reflection, cancel, reinforce, You cannot see the top image but only the bottom one.

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74 Mr Powell 2011 Index 12.6 Stationary waves on strings Specification link-up 3.2.3: Superposition of waves, stationary waves 1.What boundary condition must be satisfied at both ends of the string? 2.What is the simplest possible stationary wave pattern that can be formed? 3.How do the frequencies of the overtones compare with the fundamental frequency? Specification link-up 3.2.3: Superposition of waves, stationary waves 1.What boundary condition must be satisfied at both ends of the string? 2.What is the simplest possible stationary wave pattern that can be formed? 3.How do the frequencies of the overtones compare with the fundamental frequency?

75 Mr Powell 2011 Index Why are nodes formed in fixed positions? Hopefully you can see that as the wave passes through the reflected wave they cancel at certain points only where the phase is matched. We are in effect looking at resonance points where we can fit in parts of waves or full waves. The first or fundamental pattern can be found as 0. Then you simply work out the proportion of the wavelength that fits into L http://www.antonine- education.co.uk/physics_a2/module_4/topic_5/topic_5.htm

76 Mr Powell 2011 Index Data Table? FrequencyString Length Number of Nodes LambdaWave Speed 10.000 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100.000 1100 Ave0

77 Mr Powell 2011 Index Example Results? FrequencyString LengthNumber of NodesLambdaWave Speed 4.42.4214.8421.3 282.422 67.8 43.42.4231.6170.0 57.92.4241.2170.1 71.12.4250.9768.8 83.12.4260.8167.0 95.42.4270.6966.0 Ave68.3

78 Mr Powell 2011 Index The Real World However, the frequency of the harmonics in a real instrument may be twice, three times, four times or even more times the fundamental frequency. All these frequencies together make up the note. The bottom line here shows the wave pattern formed by the fundamental and harmonic frequencies when the note is played on the instrument. A tuning fork produces a note with only one frequency. The shape of the wave on the oscilloscope is very smooth.

79 Mr Powell 2011 Index Real Sounds We now know that we can convert our longitudinal sound wave to a transverse wave to show on a screen. If we look at these three traces of a middle C note (261Hz) we can see they are all different but seem to have similar pattern in terms of frequency as....... 1 up and 1 down takes (1/261)th of a second or the length of an arrow! You need to try an ignore the funny fluctuations, this is due to the timbre of the notes – or richness that some from the instrument itself saxophoneviolin clarinet

80 Mr Powell 2011 Index 11.5b Harmonics A tuning fork produces a note with only one frequency. The shape of the wave on the oscilloscope is very smooth.

81 Mr Powell 2011 Index Tension of Wire – Extension? By increasing the frequency of the vibrator Different stationary wave (s.w.) patterns are seen. Boundary condition for s.w.on a string is that there must be a node at each end. Velocity of a transverse wave in a wire or string: We find that.... T = Tension (N) = mass/ unit length kg/m http://hyperphysics.phy-astr.gsu.edu/hbase/waves/wavsol.html#c2

82 Mr Powell 2011 Index Extension Question A wire of mass per unit length 0.5. 10 -3 kgm -1 has a tension of 60 N and is 50 cm long. i.Calculate the velocity of any transverse wave in the wire ii.Calculate the frequency of the fundamental note. iii.If nodes are at 17cm and 34cm find the frequency of the vibrating wire. iv.What must the tension be if a note an octave above the fundamental is required? ( 2x fundamental frequency)

83 Mr Powell 2011 Index Revision… Visit the sites show below and then write a paragraph and numerical example for each. Inverse square law calculation: http://hyperphysics.phy-astr.gsu.edu/hbase/acoustic/isprob.html#c3# Geological example of sound reflection: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/mamlak.html#c2 Pitch: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/pitch.html#c1 Loudness of wave: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/loud.html#c1 String properties: http://hyperphysics.phy-astr.gsu.edu/hbase/music/stringa.html#c1 Wave properties and more : http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/soundtoc.html


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