Unit 6: Waves and Sound Brent Royuk Phys-109 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. 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 1
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 Superposition 5 Constructive vs. Destructive Interference 6 2
Interference 7 Standing Waves 8 Standing Waves How are these waveforms produced? Consider a vibrating string: 10 3
Another view: Standing Waves 11 Two-Source Interference 12 Sound Waves All sound waves are longitudinal air waves created by vibrations. 13 4
Sound Waves All sound waves are created by vibrations. 14 Sound Waves Pushing air 15 Speed of Sound v sound = (331 + 0.606 T C ) m/s 16 5
Speed of Sound v w ( ) = 331m s T 273 K 17 Speed of Sound v sound = (331 + 0.606 T C ) m/s 19 Speed of Sound v sound = (331 + 0.606 T C ) m/s Misconception: Sonic boom is heard when v s is exceeded. So does a whip break the sound barrier? The whip is tapered so transverse wave energy causes faster speeds. 20 6
Speed of Sound 21 22 Speed of Sound Speed in different media: stiffer means faster Material Speed (m/s) Aluminum 6420 Granite 6000 Plastic 2680 Fresh Water (20 0 C) 1482 Fresh Water (0 0 C) 1402 Hydrogen 1284 Air (0 0 C) 331 24 7
The Sound Spectrum Infrasonic 0-20 Hz Audible 20 Hz-20 khz Ultrasonic 20 khz-1 GHz 25 The Sound Spectrum 26 The Sound Spectrum 27 8
Sound Intensity I = Watts/m 2 Point source obeys an inverse square law So double distance equals 1/4 as much, etc. 28 Sound Intensity Threshold of hearing 10-12 W/m 2, pain threshold 1 W/ m 2 This is a big range, so we use a logarithmic scale: log I/ I o gives bels, where I o = threshold of hearing = 10-12 W/ m 2 1 db = 0.1 B β = 10 log (I/I o ) The logarithmic scale also matches human sound perception. Note that every 10 db represents a 10x increase in sound How much louder is 80 db than 60 db? Other logarithmic scales? 29 Sound Intensity 30 9
The Reflection of Sound Echoes Parabolic microphones Ultrasonic rangefinders Whispering galleries 31 The Refraction of Sound Isotherms for submarines Thermal inversion/the lake effect 32 The Diffraction of Sound 33 10
The Doppler Effect # % % 1 Moving f " = % 1 v object Source: % $ v sound means towards + means away & ( ( ( f ( ' 34 Beats Turn signals analogy The beat frequency http://library.thinkquest.org/19537/ java/beats.html 37 Musical Sound Loudness = I Equal loudness contours, next slide Pitch = f, wavelength well, almost: also depends on loudness, different for different frequencies Timbre, quality = waveform composed of pure tones Waveforms: tuning fork vs. guitar 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 38 11
Equal Loudness Contours 39 Timbre aka Quality, Color: The characteristic tone distinctive of a particular singing voice or musical instrument Physical difference: Waveform 40 Overtones 41 12
Dissecting the Waveform 42 Overtone Series 43 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 44 13
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: http://www.youtube.com/watch?v=pfs4rd5f_iq 45 Chladni Plates 46 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. 47 14
Resonance Live room standing wave patterns 48 15