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# Sound lecture part 1

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### Sound lecture part 1

1. 1. SoundThe Nature of SoundPart 1
2. 2. Mach Cone• The shape of the wake of air is knownas a Mach Cone. The width of a MachCone varies, depending on the speed ofthe object as it moves through the air.Sometimes, part of the Mach Conebecomes visible as water vapor in theair gets trapped between pressurewaves and it briefly condenses, causinga cloud of condensed vapor to form ahalo around the object.Spring 2013Thomas Jefferson: Physics2
3. 3. Spring 2013Thomas Jefferson: Physics3What IS Sound?• Sound is really tiny fluctuations of air pressure– units of pressure: N/m2 or psi (lbs/square-inch)• Carried through air at 345 m/s (770 m.p.h) ascompressions and rarefactions in air pressurewavelengthcompressed gasrarefied gas
4. 4. Spring 2013Thomas Jefferson: Physics4Properties of Waves• Wavelength ( ) is measured from crest-to-crest– or trough-to-trough, or upswing to upswing, etc.• For traveling waves (sound, light, water), there is a speed (v)• Frequency (f) refers to how many cycles pass by per second– measured in Hertz, or Hz: cycles per second– associated with this is period: T = 1/f• These three are closely related:f = vor Thorizontal axis could be:space: representingsnapshot in timetime: representingsequence at a par-ticular point in spacepressure
5. 5. Spring 2013Thomas Jefferson: Physics5Longitudinal vs. Transverse Waves• Sound is a longitudinal wave, meaning that themotion of particles is along the direction ofpropagation• Transverse waves—water waves, light—have thingsmoving perpendicular to the direction of propagation
6. 6. Spring 2013Thomas Jefferson: Physics6Why is Sound Longitudinal?• Waves in air can’t really be transverse, because theatoms/molecules are not bound to each other– can’t pull a (momentarily) neighboring molecule sideways– only if a ―rubber band‖ connected the molecules would thiswork– fancy way of saying this: gases can’t support shear loads• Air molecules can really only bump into one another• Imagine people in a crowded train station with handsin pockets– pushing into crowd would send a wave of compression intothe crowd in the direction of push (longitudinal)– jerking people back and forth (sideways, over severalmeters) would not propagate into the crowd– but if everyone held hands (bonds), this transverse motionwould propagate into crowd
7. 7. Spring 2013Thomas Jefferson: Physics7Sound Wave Interference and Beats• When two sound waves are present, thesuperposition leads to interference– by this, we mean constructive and destructive addition• Two similar frequencies produce beats– spend a little while in phase, and a little while out of phase– result is ―beating‖ of sound amplitudesignal Asignal BA + B beat(interference)in phase: addout of phase: cancel
8. 8. Spring 2013Thomas Jefferson: Physics8Speed of Sound• Sound speed in air is related to the frantic motions ofmolecules as they jostle and collide– since air has a lot of empty space, the communication that awave is coming through has to be carried by the motion ofparticles• Solids have faster sound speeds because atoms arehooked up by ―springs‖ (bonds)– don’t have to rely on atoms to traverse gap– spring compression can (and does) travel faster than actualatom motion
9. 9. Spring 2013Thomas Jefferson: Physics9Example Sound SpeedsMedium sound speed (m/s)air (20 C) 343water 1497gold 3240brick 3650wood 3800–4600glass 5100steel 5790aluminum 6420http://hypertextbook.com/physics/waves/sound/
10. 10. Speed of Sound TemperatureDependency• At normal atmospheric pressure, the temperaturedependence of the speed of a sound wavethrough dry air is approximated by the followingequation:• v = 331 m/s + (0.6 m/s/C)•T– where T is the temperature of the air in degrees Celsius.Using this equation to determine the speed of a sound wavein air at a temperature of 20 degrees Celsius yields thefollowing solution.v = 331 m/s + (0.6 m/s/C)•Tv = 331 m/s + (0.6 m/s/C)•(20 C)v = 331 m/s + 12 m/sv = 343 m/sSpring 2013Thomas Jefferson: Physics10
11. 11. 11Acoustic parameters are expressed aslogarithmic ratio of the measured value to areference valueThe Bel (B) is a unit of measurement inventedby Bell Labs and named after AlexanderGraham Bell.The Bel was too large, so the deciBel(dB),equal to 0.1 B, became more commonly used asa unit for measuring sound intensitydB SCALE
12. 12. 12Threshold of hearing 0 dB Motorcycle (30 feet) 88 dBRustling leaves 20 dB Foodblender (3 feet) 90 dBQuiet whisper (3 feet) 30 dB Subway (inside) 94 dBQuiet home 40 dB Diesel truck (30 feet) 100 dBQuiet street 50 dB Power mower (3 feet) 107 dBNormal conversation 60 dB Pneumatic riveter (3 feet) 115 dBInside car 70 dB Chainsaw (3 feet) 117 dBLoud singing (3 feet) 75 dB Amplified Rock and Roll (6 feet) 120 dBAutomobile (25 feet) 80 dB Jet plane (100 feet) 130 dBTypical average decibel levels (dBA) of some common sounds.
13. 13. Spring 2013Thomas Jefferson: Physics13Sound hitting your eardrum• Pressure variations displace membrane (eardrum,microphone) which can be used to measure sound– my speaking voice is moving your eardrum by a mere1.5 10-4 mm = 150 nm = 1/4 wavelength of visible light!– threshold of hearing detects 5 10-8 mm motion, one-half thediameter of a single atom!!!– pain threshold corresponds to 0.05 mm displacement• Ear ignores changes slower than 20 Hz– so though pressure changes even as you climb stairs, it istoo slow to perceive as sound• Eardrum can’t be wiggled faster than about 20 kHz– just like trying to wiggle resonant system too fast producesno significant motion
14. 14. Spring 2013Thomas Jefferson: Physics14Speakers: Inverse Eardrums• Speakers vibrate and push on the air– pushing out creates compression– pulling back creates rarefaction• Speaker must execute complex motion according todesired waveform• Speaker is driven via ―solenoid‖ idea:– electrical signal (AC) is sent into coil that surrounds apermanent magnet attached to speaker cone– depending on direction of current, the induced magnetic fieldeither lines up with magnet or is opposite– results in pushing or pulling (attracting/repelling) magnet incoil, and thus pushing/pulling on center of cone
15. 15. Spring 2013Thomas Jefferson: Physics15Speaker Geometry
16. 16. Spring 2013Thomas Jefferson: Physics16Push Me, Pull Me• When the center of the speaker cone is kicked, the whole conecan’t respond instantaneously– the fastest any mechanical signal can travel through a material is atthe speed of sound in the material• The whole cone must move into place well before the waveperiod is complete– otherwise, different parts of the cone might be moving in whileothers are moving out (thus canceling the sound)– if we require the signal to travel from the center to the edge of thecone in 1/N of a wave cycle (N is some large-ish number):• available time is t = 1/Nf = /Ncair• ripple in cone travels ccone t, so radius of cone must be < ccone/Ncair– basic point is that speaker size is related to wavelength of sound• low frequency speakers are big, high frequency small