Feb 2008C.M. Bali1 PHYSICS of SOUND Grade11 With CRO and Signal Generator C.M. Bali, BSc (Hons) MSc MEd Teacher Dept of Mathematics and Science (Physics) Miles Macdonell Collegiate, Winnipeg

Feb 2008C.M. Bali2 Grade 11Physics Outcomes for Sound S3P-1-17: How sounds are produced, transmitted and detected S3P-1-18: Analyze an environmental issue concerning sound S3P-1-19: Design, construct, test, and demonstrate technological devices to produce, transmit, and or control sound waves for useful purposes S3P-1-20:Intereference of sound waves. for resonance S3P-1-22: Speed of sound in air S3P-1-23: Effect of temperature and other factors (including materials) on the speed of sound. S3P-1-24: Doppler Effect (Qualitative treatment) S3P-1-25: Decibel scale (Qualitative, example of sound) S3P-1-26: Applications of sound waves (hearing aid (for Mr. Bali), ultrasound, stethoscope, cochlear implants (also perhaps for Mr. Bali)) S3P-1-28:Examine the octave in a diatonic scale in terms of frequency relationships and major triads.

Feb 2008C.M. Bali3 Cathode-ray Oscilloscope (CRO) or oscilloscope for short

Feb 2008C.M. Bali4 Sound of Music (You can even play the game Guess that Tune) Some musical instruments and their characteristic sound Click on the link below Choose the instrument Click play As you play a tune, you should display the sound pattern on the CRO. S3P1-17

Feb 2008C.M. Bali5 Experiments with CRO and signal generator 1.Frequency of a tuning fork (Slide 9) 2.Experiment to explore frequency, amplitude, pitch, intensity and loudness of Sound (Slide15) 3.Comparing loudness at different distances (Slide 18) 4.Beat Frequency (Slide 21) 5.Speed of sound using progressive waves (Slide 30) 6.Speed of sound using stationary waves (Slides 42 and 43) 7.Standing waves on strings. Speed of waves on strings (Slide 45) 8.Quality (timbre) (Slide 47) 9.How to show the velocity of a wave depends on tension and mass per unit length of string. (Slide 49) 10.Resonance (Slides 59) 11.Resonance (Slide 62) 12.Demonstration of phase and measurement of speed of sound (68) 13.Variation of intensity of sound with distance (Question) (Slide 70)

Feb 2008C.M. Bali6 The function of oscilloscope The basic function of an oscilloscope is to plot a graph of Voltage versus time

Feb 2008C.M. Bali7 Voltage versus time Voltage (Y) 1cm*5ms/cm =0.005 s 2cm*2v/cm = 2 volts 2cm*5ms/cm=10 ms =0.010 s = period Time (X) Y AMPLIFIER: 2V/cm TIMEBASE, t : 5ms/cm Timebase Ch 1Y amplifier

Feb 2008C.M. Bali8 SOUND: The maximum range of human hearing includes sound of Frequencies 15-18,000 Hz (Microsoft Encarta Encyclopedia. CD-ROM. 2000)

Feb 2008C.M. Bali9 Measurement of frequency of a tuning fork MicrophonePreamplifier Storage / Analogue switch Time base To CH 1 S3P1-17 S3p1-19 See next slide for details Save All switch

Feb 2008C.M. Bali10 Measurement of the frequency of a tuning fork 1.Connect the apparatus as in the previous slide. All switches should be in the up position. 2.Turn oscilloscope on. Adjust the intensity and focus control. 3.Timebase should be calibrated (Turn Var Sweep clockwise). 4.Strike the tuning fork and hold the prongs close to the mike. 5.Turn the time base switch until a good, well spaced, fairly stable sine signal is obtained. 6.Press Storage / analogue switch in. Freeze the trace by pressing in the Save All button. 7.Measure peak to peak horizontal distance and multiply it by time base scale. 8.Frequency = 1 / period (Hz) 9.Before repeating, press out Storage/analogue.

Feb 2008C.M. Bali11 Tuning Fork Observations T ForkTimebasePk to Pk (x) Period/secFrequency/Hz C1262 ms/cm3.9cm7.8ms = s1/0.0078=128 Hz D2881 ms/cm3.5cm3.5 ms = s1/ =285 Hz E3201ms/cm3.1cm3.1 ms=0.0031s1/0.0031= 322 Hz

Feb 2008C.M. Bali12 % Error % uncertainty

Feb 2008C.M. Bali13 Sound: Longitudinal Mechanical Waves Sound is a longitudinal wave, but they are drawn as transverse waves, to make the information clear. Sound is a mechanical wave as it requires a material medium such as air or metal or any other material for its transmission as well as a source of energy that disturbs the material medium. Click on the link below to see longitudinal and transverse waves. Pay attention to the source of disturbance and the material medium that transmits the disturbance.. Focus on any one particle (a black dot) of gas to see its to and fro movement in the direction of the flow of the waves energy: in this picture sound wave progresses horizontally to the right.

Feb 2008C.M. Bali14 Sound Characteristics Frequency Amplitude Pitch Intensity Loudness Quality or Timbre

Feb 2008C.M. Bali15 Experiment to explore frequency, amplitude, pitch, intensity and loudness of Sound MicrophonePreamplifier Time base To CH 1 Speaker Signal Generator Constant distance Frequency dial Amplitude dial Frequency display See next slide for details D S3P-1-19,1-27

Feb 2008C.M. Bali16 Frequency and Pitch Set up the experiment as in the previous slide (15). Turn on the oscilloscope and the signal generator. Investigate the pitch by listening to the sound from the speaker as the frequency is increased and then decreased. Keep amplitude (peak to peak distance on the oscilloscope) and D constant. Students should see that the higher the frequency the higher the pitch. (You can do this by using tuning forks of various frequencies, but it is difficult to keep the amplitudes constant) S3P-1-27

Feb 2008C.M. Bali17 Intensity and loudness of Sound See slide # 10 for experimental set up. Intensity = power per m 2 (W m – 2 ) Power is proportional to the square of the amplitude of the wave. (Follows from SHM) Amplitude of the CRO trace is proportional to the amplitude of the sound wave hitting the microphone. Thus intensity of sound is proportional (not equal) to the square of the amplitude of the CRO trace. [CRO measures voltage] Loudness: S3P-1-27

Feb 2008C.M. Bali18 Comparing loudness at different distances Set up the experiment as shown below (also see slide 10). Place microphone 50 cm from the speaker and adjust the volume on the signal generator to get a CRO trace of 1 cm amplitude. Move the microphone by 20 cm at a time towards and away from the speaker. Find the dB level of the sound relative to the reference point. Microphone Speaker 50 cm100cm 0 cm Signal generator Distance = 50 cmA (50) = 1. 0 cmRelative Loudness = 0 dist = 30A (30) =dB = 20 * log {A(50) / A(30)} = dist = 10 cmA(10) = dist = 70A(70)- = dist = 90 cmA(90) = S3P-1-27

Feb 2008C.M. Bali19 Double Beam Oscilloscope It has two inputs CH1 CH2 and a common timebase Therefore, you can display and compare two signals (graphs) simultaneously.

Feb 2008C.M. Bali20 Beat Phenomenon When two sound waves of different frequencies interfere we hear sound whose amplitude varies periodically.

Feb 2008C.M. Bali21 How to show beat phenomenon and measure beat frequency Signal Gen 1 Signal Gen 2 To Red and Black terminals To red and black terminals To CH1 To Ch 2 Speaker 1Speaker 2 499Hz 510Hz Timebase Measure Beat period Beat period Store All switch Storage / analogue switch Bt freq = 1 / Bt period Ch1, Ch2, Dual, Add SWITCH Outcomes SP Sp S3P-1-20 See slide 26 for details

Feb 2008C.M. Bali22 Measurement of beat frequency When two sinusoidal functions of different frequencies are added we get: Time Displacement TbTb

Feb 2008C.M. Bali23 Beat Frequency Formula If two sinusoidal disturbances, y1 and y2, of frequencies, f1 and f2, are added, the principle of superposition gives : Not for grade 11students but suitable for grade 12

Feb 2008C.M. Bali24 Beat Frequency Formula: A simple approach using relative speed Imagine two athletes, A and B, running to and fro on a straight track, a total distance of 2L. Suppose A takes x seconds and B takes y seconds to complete one to and fro distance on the track. Therefore, x and y are the periods of A and B Frequency of A =1/x, and of B= 1/y Let us assume they will be running for some time! We want to know how often they meet or cross each other. To be more precise, how many times per second they will cross each other; that is, what is their beat frequency? Students should be able to do this proof SP3-1-20

Feb 2008C.M. Bali25 Beat Frequency Formula: A simple approach using relative angular speed (in degrees) Imagine two athletes, A and B, running around a circular track. Suppose A takes x seconds and B takes y seconds to go round the track once. Therefore, x and y are the periods of A and B Frequency of A =1/x, and of B= 1/y Let us assume they will be running for some time! We want to know how often they cross each other. To be more precise, how many times per second they will cross each other; that is, what is their beat frequency? You can go through this argument using radians, and will get the same result. Students should be able to do this proof

Feb 2008C.M. Bali26 Measurement of Beat frequency Experimental Procedure 1.Set up the experiment as in slide Set Signal 1 to 490 Hz, and Signal 2 to 509 Hz. You should hear beating sound. 3.Set Oscilloscope to: Dual, time base to 20ms/Div, Storage/ analogue switch in, and Y1 and Y2 to an appropriate scale. You should see two traces somewhat out of phase. 4.Now press the Add switch. 5.With the storage / analogue switch in, Press Store All switch. 6.This should freeze the trace. 7.Measure Beat period. 8.Calculate Beat frequency.

Feb 2008C.M. Bali27 Beat Frequency Observations Speaker 1 Freq / Hz Speaker 2 Freq / Hz Time baseBeat period Beat period /seconds Beat frequency/ Hz ms/ cm 5.6 cm0.050*5. 6=0.280 s 1/0.280= 3.57= 4Hz 201 This was a good graph ms/cm 5.4cm0.108 s9.25 Hz 1010 This was a good graph ms/ Div 4.5cm0.090 s11 Hz

Feb 2008C.M. Bali28 Sound as Progressive wave A simple argument for students Progressive waves carry energy from one point to another. As the wave particle oscillates once, the wave moves forward by one wavelength. If the particles oscillates f times per second, the wave will move forward f wavelengths. Thus:

Feb 2008C.M. Bali29 Speed = frequency * wavelength A more rigorous derivation Not for students

Feb 2008C.M. Bali30 Measurement of speed of sound using progressive waves A B C E F 0cm 100 cm A = Signal generator B = Speaker C = Mini Microphone D = Block of wood for support E = Preamplifier F = Mitre rule D Note this reading when both signals are in Phase Move D until both signals are in phase again. Note this point This distance, d = One wavelength Timebase Frequency can be read Directly from Signal generator Or from the oscilloscope trace To Ch1 input To Ch2 Double beam S3P- 1-17, 1-19, 1-22 See slide 32 for details Dual mode

Feb 2008C.M. Bali31 Measurement of speed of sound Using progressive waves 1.Set up the experiment as shown on the previous slide 2.We know from basic experiments that speed of sound is about 340 m / s. 3.We want to measure a wavelength of say 20 cm. This informs us that the frequency should be around 340 / 0.20 = 1700 Hz. 4.We will use the frequency of sound at 1.5 KHz to 3.0 kHz. Sig. Gen freqFreq from CROWavelengthSpeed using CRO freq % uncertainty 1470 Hz( ) = cm0.24*1470 = 3 50 m / s About 5% 1960 Hz(36-0)/2 = 18cm0.18*1960 = 352 m / s See next two slides 2439 Hz = 14.5 cm0.145 * 2439 = 353 m / s 2940 Hz = 11.6 cm340 m/sec

Feb 2008C.M. Bali32 Errors and uncertainties Students can calculate errors and uncertainties in the beat frequencies from data in previous slide

Feb 2008C.M. Bali33 How to calculate uncertainties

Feb 2008C.M. Bali34 Calculating Uncertainties Sig. Gen freqFrequency from CROWavelengthSpeed using CRO freq 1500 Hz 1470 Hz( ) = cm0.24*1470 = 3 50 m / s

Feb 2008C.M. Bali35 Theory of Uncertainties Errors always add, hence absolute signs. Not for students

Feb 2008C.M. Bali36

Feb 2008C.M. Bali37 Uncertainties A measurement can never be perfect. The minimum error in a measurement is equal to the instrumental error. If the variation in the measurement is much bigger than the instrumental error, then ignore the instrumental error, but use the deviation or standard deviation from the mean as a measure of uncertainty in the mean.

Feb 2008C.M. Bali38 Example

Feb 2008C.M. Bali39 Conditions for setting up Stationary Waves When two progressive waves of the same frequency and wavelength And traveling in opposite directions And interfere then, at certain wavelengths, that satisfy the boundary conditions, Stationary waves are formed.

Feb 2008C.M. Bali40 Mathematics of Stationary Waves Not for grade 11 students

Feb 2008C.M. Bali41 Standing waves From the University of Toronto erest/Harrison/Flash/#sound_waves

Feb 2008C.M. Bali42 Speed of sound using stationary waves Speaker Signal GeneratorAmplitude dial See next slide for details S3P-1-19,1-27 Shiny reflector Microphone Dual Mode Speaker signal Microphone signal (White dotted line): almost flat showing a node position at microphone CH 1 CH 2

Feb 2008C.M. Bali43 Speed of sound using Stationary Waves 1.Set up the experiment as in the previous slide (slide 42) 2.Move the screen until the microphone signal is very small (see slide 45 for analogy). 3.Now keep the screen still, and move the microphone gently. 4.Measure the distance between two nodal points: this is equal to the distance moved by the microphone between two successive points where the CRO signal is very small, while the reflector is kept at the same position. This distance is equal to half the wavelength. Thus, the wavelength is twice this distance. 5.Find speed of sound by multiplying the wavelength by the frequency, which can be seen on the signal generator. 6.Find uncertainty in the speed. 7.Find error in the speed. DistanceWavelengthFrequencySpeeduncertaintyError

Feb 2008C.M. Bali44 Natural Frequencies and Resonance All objects have certain natural frequencies of oscillations. For example, a swing can oscillate back and forth at a certain frequency that depends on its dimensions. If you push this swing gently but periodically, such that the frequency of your push is exactly the same as the natural frequency of the swing, then energy can flow from the your body into the swing. The energy in the swing can build up to the extent that the swing may become very unstable (very high amplitude of vibration) and even break !! Three dimensional objects have many natural frequencies of vibrations. Show: Tacoma Narrows Bridge Falls bridge-p1.php The phenomenon in which energy can pass easily from one object (A) into an other (B) if it is fed at the natural frequency of the other (B) object is called resonance. SEE NEXT SLIDE:

Feb 2008C.M. Bali45 How to set up a stationary (resonating) wave on a string B A D E A: Signal Generator B: Vibrator C; String D Pulley E: Weight to provide tension in string Table C 1 st Harmonic 2 nd Harmonic 3 rd Harmonic 4 th Harmonic Vibrates with small amplitude Large amplitude of vibration S3P-1-21 AN N N N

Feb 2008C.M. Bali46 Harmonics and Overtones See Previous Slide 45 for experimental set up. 1.Look at the frequency on the signal generator as you set up stationary waves on the string. 2.The frequency is lowest when first harmonic is set up. This frequency is called the fundamental frequency. 3.As the number of harmonics increases, frequency increases. (note: the nth harmonic has n half waves.) 4.OVERTONES: When an instrument (e.g. a taut wire as in the experiment) is plucked, it produces a sound which is a combination of many harmonics. 5.Overtones can be displayed on the CRO and analyzed and shown to be composed of harmonics of that taut wire. 6.The first overtone is the first harmonic, the second overtone is the second harmonics, and so on. S3P-1-27

Feb 2008C.M. Bali47 Quality or Timbre of Sound When an instrument is played it does not produce a note of just one frequency. It consists of the fundamental frequency and higher harmonics with different amplitudes. The resultant wave is the superposed sum of various harmonics. Thus the resultant wave is different from that of the fundamental frequency. The ear responds to the fundamental frequency, but it also senses the presence of higher harmonics. This sensation due to the presence of many harmonics is called the quality of sound. Thus different instruments, and even the same instrument, generate sounds of different quality, even though they may be playing the same fundamental frequency. Play a tune from slide 4 and observe the trace on the CRO

Feb 2008C.M. Bali48 Analysis of Quality or Timbre of Sound With a graphing calculator Use TI83 or the link below for a graphing calculator: Without Fourier analyzing, we can see that a periodic non-sinusoidal function is the sum of many sinusoidal functions. Graphing Calculator: Set window to : x min (-5), x max (5), y min (-2), y max (2); Xscl and Yscl =0.1 Mode Radians. Example: draw a graph of: Y = 1sin (x) sin (2x) + 0 sin (3x) sin (4x) : You should see that Y is periodic but non-sinusoidal, the period being different from the periods of the component harmonics, (also draw individual graphs) Thus quality is due the presence of many harmonics.

Feb 2008C.M. Bali49 Experiment The speed of a wave on a string Set up the experiment as in slide 45. Record resonant frequency for the first, second and third harmonic. Enter the observations in the table below. Find average speed. Different students can try same material of different thicknesses and tensions. Precautions: Keep tension constant. Check L has not changed. Length of string, L / m N = Number of loops, or harmonics wavelength = 2L/(N) / m Freq, f / Hz (from Sig. Gen) v = freq * wavelength (m / s)

Feb 2008C.M. Bali50 An Experiment for IB or AP Students Problem: The speed of a wave on a string is thought to depend on the tension in the string. Investigate the relationship between speed and tension. Idea: Let us suppose that the speed depends on the tension. We dont know how it depends. [Theory must always precede experiment, even if we dont realize it.] So assume – requires some thought!

Feb 2008C.M. Bali51 Theory and Analysis of data

Feb 2008C.M. Bali52 Experimental details Set up the experiment as shown in slide 45. Conduct the experiment in second harmonic. Keep the length of the string constant. Apply different weights to vary the tension. For each weight, note f on signal generator. The wavelength is L. Therefore the speed of the wave is f * L. Record the observations in the table below:

Feb 2008C.M. Bali53 Data Mass / kg Weight (mg) / N Wavelength / m Frequency / Hz Speed m /s

Feb 2008C.M. Bali54 Graph of ln(V) vs. ln(T) ln (T) ln (v) Gradient = 0.5 O ln (K)

Feb 2008C.M. Bali55 Discussion Conclusion At a more simple level, students can plot Velocity versus Sqrt of T. A straight line of slope 1will uphold the relationship between velocity and tension.

Feb 2008C.M. Bali56 Velocity and mass per unit length ln v Slope should be – 1/2

Feb 2008C.M. Bali57 Experimental details Set up the experiment as in slide 45. You should use wires of the same material but different thicknesses. Use the same length of wire, keep tension the same. Do experiment in 2 nd harmonic to keep calculations easy – this makes wavelength = L Plot L / mMass/mTension Constant f / Hz 2 nd Harmonic V = f * Lln V ln (mass /m)

Feb 2008C.M. Bali58 Analysis Graph Calculations of slope etc Discussion Conclusion.

Feb 2008C.M. Bali59 Resonance Measurement of speed of sound using a resonance tube Demonstration of nodes and antinodes with sound RBRB FAFA Speaker Oscilloscope Preamp Mike Tube Signal generator Freq dial Amplitude dial L = wavelength / 4 Metre rule To Ch 1 or 2 Shows Large signal At Resonance To show node at the bottom gently lower the microphone to the bottom of the cylinder SP3-1-20, 1-21, 1-22

Feb 2008C.M. Bali60 Data

Feb 2008C.M. Bali61 Discussion of results: Note: Accepted value= T/degC So at room temp, v =332+.6*20=344 m / s End Correction: depends on the tube diameter Measurement techniques, including parallax Include % error Conclusion:

Feb 2008C.M. Bali62 Resonance Measurement of speed of sound using a resonance tube Demonstration of nodes and antinodes with sound RBRB FAFA Speaker Oscilloscope Preamp Mike Tube Signal generator Freq dial Amplitude dial Metre rule To Ch 1 or 2 Shows Large signal At Resonance n = number of loops or harmonics, here n = 1 Tube open at both ends SP3-1-20, 1-21, 1-22

Feb 2008C.M. Bali63 Resonance Tube ( both ends open) Observations First resonant frequency =359 Hz Length of tube = 45.5 cm

Feb 2008C.M. Bali64 Phase relationships and oscilloscope Consider two functions (or voltage signals) y (t) and x (t) where:

Feb 2008C.M. Bali65 The principle of superposition gives: Case 1: Phase Difference (1) (2) R=Resultant displacement as a function of time A relation independent of time, or true at all times Y-axis X-axis

Feb 2008C.M. Bali66 Case 2 : Phase Difference cos180 = -1, and sin180 = 0 Therefore, Lissajous relation X-axis /cm Y-axis Timebase off, X-Y in Time Y cm

Feb 2008C.M. Bali67 Case 3 : Phase Difference cos 90 = 0, and sin 90 = 1 Therefore, Lissajous relation X-axis /cm Y-axis Timebase off, X-Y in

Feb 2008C.M. Bali68 How to demonstrate change in phase Speed of sound using this method. A B C E F 0cm A = Signal generator B = Speaker C = Microphone D = Block of wood for support E = Preamplifier F = Mitre rule D Timebase To Ch1 input To Ch2 Double beam Move the microphone, with the X-Y switch pushed in The trace should change: you should see straight line (+ & - slope) and circle Wavelength = distance moved by the microphone for the phase to change by 2pi radians. X-Y switch Pressed IN

Feb 2008C.M. Bali69 X-axis Y-axis With time base off, And X -Y switch in Sine function with double amplitude X-Y switch out, timebase on Lissajous Figure Add Switch on Sine function with Zero amplitude

Feb 2008C.M. Bali70 Question How would you investigate the variation of sound intensity with distance? Signal Gen Speaker 1 Timebase Store All switch Storage / analogue switch Ch1 Pre Amplifier Microphone Distance = x

Feb 2008C.M. Bali71 Doppler Effect Use internet sources to demonstrate this effect S3P-1-24

Feb 2008C.M. Bali72 End C.M. Bali, BSc (Hons) MSc MEd CPhys MInstP Teacher Dept of Mathematics and Science (Physics) Miles Macdonell Collegiate, Winnipeg, Canada