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Chapter 17/16: Waves & Sound

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Chapter 17/16: Waves & Sound Chapter 17/16: Waves & Sound Brent Royuk Phys-112 Concordia University Waves • What is a wave? • Examples – Water, sound, slinky, ER • Transverse vs. Longitudinal 2 Wave Properties • The magic of waves. – Great distances – What are they made of? • Wave Anatomy – Crest, trough, speed, frequency, wavelength, amplitude, period. • The Wave Equation: v = fλ – What is the wavelength of a sound wave produced by a violin playing the note A above middle C when the speed of sound is 350 m/s? 3 The Four Wave Behaviors 1. Reflection – Waves bounce off obstacles 2. Refraction – Waves bend when entering a new medium at an angle. 3. Diffraction – Waves bend around corners and spread out from small openings. 4. Superposition (Interference) – Waves pass through each other, and their amplitudes add. 4 Sound Waves • All sound waves are longitudinal air waves created by vibrations. 5 Sound Waves • All sound waves are longitudinal air waves created by vibrations. 6 Sound Waves • All sound waves are created by vibrations. 7 Sound Waves • Tuning Fork Vibrations 8 Sound Waves • Pushing air 9 Speed of Sound T vw = 331m s ( ) 273 K € 10 Speed of Sound 11 Speed of Sound T vw = 331m s ( ) 273 K € 12 Speed of Sound • vsound = (331 + 0.606 TC) m/s 13 Speed of Sound • vsound = (331 + 0.606 TC) m/s 14 Speed of Sound T vw = 331m s ( ) 273 K € The crack of the bat 15 Speed of Sound 16 17 18 Speed of Sound • Speed in different media: stiffer means faster Material Speed (m/s) Aluminum 6420 Granite 6000 Plastic 2680 Fresh Water (200 C) 1482 Fresh Water (00 C) 1402 Hydrogen 1284 Air (00 C) 331 19 The Sound Spectrum • Infrasonic 0-20 Hz • Audible 20 Hz-20 kHz • Ultrasonic 20 kHz-1 GHz 20 The Sound Spectrum 21 The Sound Spectrum 22 Sound Intensity • I = Watts/m2 – Point source obeys an inverse square law • So double distance equals 1/4 as much, etc. 23 Sound Intensity • Threshold of hearing ≈ 10-12 W/m2, pain threshold ≈ 1 W/m2 • This is a big range, so we use a logarithmic scale: log I/Io gives bels, where Io = threshold of hearing = 10-12 W/m2 – 1 dB = 0.1 B – β = 10 log (I/Io) • Examples – Find dB for I = 3 x 10-5 W/m2 – Find dB for I = 4.8 x 10-10 W/m2 • Note that every 10 dB represents a 10x increase in sound energy but not perceived loudness. 10 dB is ~twice the perceived loudness. – How much louder is 80 dB than 60 dB? • Other logarithmic scales? 24 Sound Intensity 25 The Reflection of Sound • Echoes • Parabolic microphones • Ultrasonic rangefinders 26 The Reflection of Sound • Whispering galleries 27 Whispering Gallery 28 The Refraction of Sound • Isotherms for submarines • Thermal inversion/The lake effect 29 The Diffraction of Sound 30 The Doppler Effect 31 The Doppler Effect Moving " % " % Stationary vw ± v obs Source: vw f f f f Source: obs = s $ ' obs = s $ ' v v ± v # w & # w s & – towards + towards + away - away € € 32 The Doppler Effect 33 Superposition 34 Constructive vs. Destructive Interference 35 Interference 36 Sound Canceling 37 Standing Waves 38 Standing Waves • Getting started: 39 Standing Waves • Nodes, antinodes, fundamental, harmonics 40 Standing Waves fn = nf1 λ1 = 2L 41 € The Harmonic Series Sound Waves in Pipes 42 Example • A guitar string 60 cm long vibrates with a standing wave that has three antinodes. (a) Which harmonic is this? (b) What is the wavelength of this wave? (c) If this harmonic is excited with a frequency of 600 Hz, what is the frequency of the fundamental? 43 Standing Waves 44 Drum Modes Animations courtesy of Dr. Dan Russell, Kettering University 45 Drum Modes 46 Closed Pipe Resonance v f = n w ,n = 1,3,5… Nodes & Antinodes n 4L Example 17.5, p. 606 47 € Beats • Turn signals analogy • The beat frequency • http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ ClassMechanics/Beats/Beats.html • Wave simulator: https://phet.colorado.edu/en/simulation/wave-interference 48 Musical Sound • Loudness = I – Equal loudness contours • Pitch = f, wavelength – well, almost: also depends on loudness, different for different frequencies • Timbre, quality = waveform – oscilloscope: tuning fork vs. guitar – composed of pure tones – Harmonics (on guitar): overtones – Different instruments have different overtones, thus different timbre • e.g. closed pipes only have even overtones, duller than open pipes • Different resonators: wind, string, percussion comparisons 49 Equal Loudness Contours 50 Timbre 51 Timbre 52 Timbre 53 Timbre 54 Guitar Timbre 55 Guitar Timbre 56 Violin Timbre 57 Timbre • Interactive Synthesizer 58 Timbre 59 Harmony • Integral multiples of a frequency reinforce each other • The harmonic series – 128 C below middle C – 256 middle C – 384 G above middle C – 512 C above middle C – 640 E – 768 G – 896 B flat – 1024 C again 60 Harmony • Harmonic Intervals and the Overtone Series 61 Resonance • Resonance tubes • Singing rods • Resonant room frequencies – A room's fundamental resonant frequency can be calculated by dividing the speed of sound in feet per second (1130) by twice the length. • Chladni Plates 62 Resonance 63 Resonance 64 Resonance 65 Resonance • Tacoma Narrows Bridge Collapse – The first Tacoma Narrows Bridge opened to traffic on July 1, 1940. Its main span collapsed into the Tacoma Narrows four months later on November 7, 1940, at 11:00 AM (Pacific time) due to a physical phenomenon known as aeroelastic flutter caused by a 67 km/h (42 mph) wind. The bridge collapse had lasting effects on science and engineering. In many undergraduate physics texts the event is presented as an example of elementary forced resonance with the wind providing an external periodic frequency that matched the natural structural frequency (even though the real cause of the bridge's failure was aeroelastic flutter). – No human life was lost in the collapse of the bridge. However, a small do perished after it was abandoned in a car on the bridge by its owner, Leonard Coatsworth, and by another man, both of whom were bitten by the terrified dog when they attempted to remove it. 66 Resonance • Live room standing wave patterns • Simulation 67 Rubens Tube 68 Resonance • 3-D standing wave patterns 69.
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