Outline. Sound Waves. A. The Nature of Waves. 1. Types of Waves. 1. Types of Waves. 2. Structure of a wave. 3. Seismography.

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1 The Science of Sound Lecture Sound Waves Updated 008 Jan 1 Dr. Bill Pezzaglia Physics SCU Outline A. Nature of Waves 1. Types of Waves. Structure of Waves 3. Seismography B. Wavespeed 1. Measurement of speed of sound. Theoretical Calculation of Wavespeed 3. Doppler Effect C. Reflection 1. Total Reflection. Partial Reflection 3. Reflectivity and Impedance D. Refraction 1. Fermat s problem: the path of least time. Snell s Law for angle of refraction 3. Sound bent by change in temperature of air E. Diffraction 1. Interference of Sound. Huygen s Principle of wave propagation 3. Diffraction through a slit (e.g. sound through a doorway) F. References A. The Nature of Waves 1. Types of Waves. Structure of a wave 3. Seismography 3 1. Types of Waves (a) Longitudinal ( p waves) travel through gas, liquid and solids. Particle motion in direction of wave (b) Transverse ( s waves) travel only in solids. Particle motion perpendicular to direction of wave. 4 (c) Ocean Waves Ocean Waves are Cycloid Waves. Particles travel in circles. 5 (d) Surface Waves Rayleigh Waves ( R wave) are similar, but exist in solids (more damaging in earthquakes than p or s waves) 6 Similar type (gravity) waves in the atmosphere, seen from above (starting at a volcano) Love Waves ( Q wave) are sideways surface vibrations, and are the most destructive in earthquakes 1

2 (e) Light Waves Light is a wave of electric and magnetic phenomena that can travel through empty space (no medium!) 7 (f) Gravity Waves? Not discovered yet, but we are looking for them. They would distort space as they travel by! 8 (g) LIGO Laser Interferometer Gravitational-Wave Observatory is looking for them! 9. The Structure of a Wave a) Structure i. Nodes: no displacement 10 ii. Antinode: maximum displacement b) Measurement of Wave i. Wavelength (measured in meters) ii. Amplitude (loudness) is the maximum wave displacement 11 c. Sound is displacement of pressure 1 (i) Rarefaction: the trough of the wave where pressure(density) is low (ii) Compression: the peak of the wave where pressure(density) is high

3 d) Frequency Frequency f : oscillations per second (Hertz) Wavespeed c : is frequency x wavelength c = fλ 13 3a Seismographs AD: Chinese (Zhang Heng) have primitive device 1880 John Milne invents modern seismograph (shear waves) 3b Two Basic Wave Types (Andrija Mohorovičić 1909) 15 3c Liquid Core 16 (pressure waves) Richard Dixon Oldham (July 31, 1858 July 15, 1936) was a British geologist who, in 1906, argued that the Earth must have a molten interior as S waves were not able to travel through liquids nor through the Earth's interior. S Shadow Zone (shear waves) S waves can only travel in solids! P can travel in solid, liquid and gas! 3d Speed of Waves 17 3e. Velocities of P and S waves in different layers of the Earth 18 Beno Gutenberg 1914 (worked with Richter) determines travel times for waves. Measures Temp and pressure inside of earth Measures size of core from P Wave Shadow Zone. P wave velocities: in granite: 6 km/sec in basalt: 7 km/sec in peridotite: 8 km/sec 3

4 3f Reflection & Refraction 19 Seismic waves are reflected or bent at the boundaries of different layers inside the earth 3g. Solid Inner Core (1936) The pressure at the center of the Earth is 3.6 million atmospheres Solid inner core discovered 1936 by Inge Lehmann from reflection/refraction of waves (for a time called the Lehmann discontinuity). Size not determined until 1960s from shockwaves from underground nuclear tests (echoes bouncing off inner core). 0 B. Wavespeed 1 1a. Leonardo da Vinci 1. Measurement of Speed of Sound Speed of sound is finite. Theory Calculation of speed 3. Doppler Effect A bell far away, will be heard to resonate in response to a bell ringing, after a delay in time Did he measure the speed of sound? (some references say yes) AD 1b Speed of sound depends upon medium! 3 1c William Derham ( ) 4 (1640) classic experiment on the sound radiation by a ticking watch in a partially evacuated glass vessel provided evidence that air is necessary, either for the production or transmission of sound. First to accurately measure speed of sound. (341 meters/second) Newton used his value in the Principia (1686), although it was 16% higher than the value Newton theoretically calculated. Robert Boyle ( AD) 4

5 1d Speed of Sound in Water (186) 5. Theory of Speed of Sound 6 Ion Lake Geneva, Switzerland, Jean- Daniel Colladen, a physicist, and Charles-Francois Sturm, a mathematician, measured speed to be 5x faster than in air. In their experiment, the underwater bell was struck simultaneously with ignition of gunpowder on the first boat. The sound of the bell and flash from the gunpowder were observed 10 miles away on the second boat. The time between the gunpowder flash and the sound reaching the second boat was used to calculate the speed of sound in water. Speed did NOT depend upon frequency! (a) Speed of sound depends upon the properties of the medium through which it travels: B coefficient of stiffness (springiness) measured in Pascals (the unit of pressure, Newton/meter ) ρ density (kilograms per cubic meter) c speed in meters/second c = B ρ b. Speed of Sound in Gas, Liquid and Solid 7 Note generally speed in solid > speed in liquid > speed in gas Item B (Pa) ρ (kg/m 3 ) V (m/s) Air Water Ice c. Speed in Gas Speed of sound depends upon T Temperature (Kelvin), faster when hot m molecular mass (kg/mole) Heavier gas slower (CO) Lighter gas faster (Helium) γ Fudge Factor (7/5) c = γ RT m 8 Iron R gas constant Joules/ K Mole 3. Doppler Effect 184 Christian Doppler shows detected frequency f d depends upon: f f s frequency of source d fs 1 v relative speed between detector and source c velocity of sound in medium So if moving 10% speed of sound towards you, the frequency will be increased 10% 9 v = + c C. Reflection 1. Total Reflection. Partial Reflection Acoustic Impedance 5

6 1. Total Reflection 31. Partial Reflection 3 Wave hitting a perfect mirror will be reflected Reflected wave is inverted. Wave passing from one medium to another will be partially reflected. Some of the wave is transmitted through 3. Specific Acoustic Impedance Z1 Z The amount of reflected energy: R = Z1 + Z Z is the specific acoustic impedance (resistance to vibration) Z = ρ B = ρ c So 99.95% of sound is reflected between air/water (hence you can t hear fish talking from above water) 33 D. Refraction 1. Fermat s Principle of Least Time. Snell s Law (161) 34 Item B (Pa) ρ (kg/m 3 ) Z (rayls) 3. Sound bent by Temperature Air Water glass Fermat s Principle 35. Snell s Law (161) 36 Lifeguard Dilemma: What is the fastest path to drowning man? Note you can run twice as fast as you can swim. Run straight to river, then swim Run further to shore adjacent swimmer then swim Optimal path obeys Snell s Law The path light (sound) takes is the one of minimum time Lifeguard Tower 1 1 sinθ1 = sinθ v v 1 Path of sound is bent toward normal when enters media with lower wavespeed (i.e. lower density) 6

7 3. Bending by Temperature 37 E. Diffraction 38 a) Velocity of sound increases with temperature: v b) Warm air over cool lake will bend sound down c) Cool air over hot road will bend sound up T 1. Huygen s Principle. Interference 3. Young slit diffraction 1. Huygen s Principle (1678) 39. Interference Two waves added together can cancel each other out if out of phase with each other. 40 Combined Wave Wave 1 Wave Coherent waves (in phase) add together to make bigger wave Waves 180 out of phase will cancel each other! 3. Diffraction Patterns Two wave sources close together (such as two speakers) will create diffraction patterns. At certain angles the waves cancel! 41 F. References Wave Animations: Huygen s Animation: Hugens & Diffraction More animations Water Waves 4 7

8 Demos Boyle: sound in vacuum Bottle (speed of sound) Temperature (use hairdryer) Molecular mass (canned air) Doppler Demo Rope high and low mass (reflection) Diffraction transparencies Diffraction (two speakers, need sound source) Perhaps use identical tuning forks? Si l t? 43 8