1Wed. Feb. 21 Phy107 Spr07 Lect 131From Last Time… Wave Properties• Amplitude is the maximum displacement ofstring above the equilibrium position• Wavelength, λ, is the distance between twosuccessive points that behave identically• Period: time required to complete one cycle• Frequency = 1/Period = rate at which cyclesare completed• Velocity = Wavelength/Period,v = λ / T, or v = λfWed. Feb. 21 Phy107 Spr07 Lect 132Vibrations of basilarmembrane• Different locations hostbundles that senddifferent pitch signals.Wed. Feb. 21 Phy107 Spr07 Lect 133Pitch• Pitch is related mainly, although notcompletely, to the frequency of the sound• Pitch is not a physical property of the sound• Frequency is the stimulus and pitch is theresponse– It is a psychological reaction that allows humansto place the sound on a scaleWed. Feb. 21 Phy107 Spr07 Lect 134Frequency Response Curves• Bottom curve is thethreshold of hearing– Threshold of hearing isstrongly dependent onfrequency– Easiest frequency to hear isabout 3000 Hz• When the sound is loud(top curve, threshold ofpain) all frequencies canbe heard equally wellWed. Feb. 21 Phy107 Spr07 Lect 135Timbre• In music, the characteristic sound of anyinstrument is referred to as the quality ofsound, or the timbre of the sound• Not all sound is a pure tone.• The quality depends on the mixture of‘harmonics’ in the sound.• This is a mixture of other frequencies with theoriginal.• Can completely describe the sound by onlyincluding ‘overtones’Wed. Feb. 21 Phy107 Spr07 Lect 136Quality of Sound – Tuning Fork• Tuning fork producesonly thefundamentalfrequency2Wed. Feb. 21 Phy107 Spr07 Lect 137Quality of Sound – Flute• The same note played on aflute sounds differently• Not a pure tone=++Fundamental,Freq. f1st harmonic,Freq. 2f2nd harmonicFreq. 3fWed. Feb. 21 Phy107 Spr07 Lect 138Quality of Sound – Clarinet• The fifth harmonic isvery strong• The first and fourthharmonics are verysimilar, with the thirdbeing close to themWed. Feb. 21 Phy107 Spr07 Lect 139Combining waves• Many sounds are superpositions of differentcontributions• Waves obey the Superposition Principle– If two or more traveling waves are moving through amedium, the resulting wave is found by addingtogether the displacements of the individual wavespoint by point– Constructive interference: waves reinforce– Destructive interference: waves tend to cancelWed. Feb. 21 Phy107 Spr07 Lect 1310Constructive Interference in a String• Two pulses are traveling inopposite directions• The net displacement whenthey overlap is the sum ofthe displacements of thepulses• Note that the pulses areunchanged after theinterferenceWed. Feb. 21 Phy107 Spr07 Lect 1311Constructive Interference• Two waves, a and b, havethe same frequency,amplitude, and start point– Are in phase• The combined wave, c, hasthe same frequency and agreater amplitudeCombined wave+=Wed. Feb. 21 Phy107 Spr07 Lect 1312Destructive Interference in aString• Two pulses are traveling inopposite directions• The net displacement whenthey overlap thedisplacements of the pulsessubtract• Note that the pulses areunchanged after theinterference3Wed. Feb. 21 Phy107 Spr07 Lect 1313Destructive interference in acontinuous wave• Two waves, a and b, havethe same amplitude andfrequency• They are 1/2 wavelengthout of phase• When they combine, thewaveforms cancel+=Wed. Feb. 21 Phy107 Spr07 Lect 1314Interference• Water drop is a source ofcircular waves (two-dimensions here)• When the waves overlap,they superimpose.• In some areas they cancel,in others they reinforce.• This is called interferenceWed. Feb. 21 Phy107 Spr07 Lect 1315QuestionBelow are sound waves to be added together. Whichset results in a quieter sound?A. AB. BC. Both sameABWed. Feb. 21 Phy107 Spr07 Lect 1316Interference of sound waves• Interference arises when waves change their‘phase relationship’.• Can vary phase relationship of two waves bychanging physical location of speaker.ConstructiveDestructive‘in-phase’‘1/2 λ phase diff’Wed. Feb. 21 Phy107 Spr07 Lect 1317Superimposing sound waves• Depending on your relat ive distance fromtwo identical sound sources, the soundintensity can vary.• Important aspect is relative distance fromeach source in wavelengths!Wed. Feb. 21 Phy107 Spr07 Lect 1318QuestionTwo speakers each emit a 340 Hz sound wave.At what separation of these speakers wouldyou hear a quieter sound by turning on oneof the speakers?A. 0.1 mB. 0.25 mC. 0.5 mD. 1.0 mE. 2.0 m4Wed. Feb. 21 Phy107 Spr07 Lect 1319Interference of 2 speakerscresttroughconstructiveinterference,loud tonedestructiveinterferencequit toneWed. Feb. 21 Phy107 Spr07 Lect 1320InterferenceengineeringWed. Feb. 21 Phy107 Spr07 Lect 1321Line array works by interference• Off-axis sound canceled by interference on thevertical axis.• Horizontal plane unaffected• Total sound intensity drops off more slowlyWed. Feb. 21 Phy107 Spr07 Lect 1322Destructive interference• Two speakers playing the same tone togethercan be quieter each than individually!Destructive‘1/2 wavelength phase diff’Destructiveinterference forfrequencies such thatpath lengthdifference is 1/2wavelength.Wed. Feb. 21 Phy107 Spr07 Lect 1323QuestionIn your room you have two speakers in differentcorners. At your desk you are exactly 1 meter fromeach, so that there is no interference. Yourroommate moved one of your speakers 0.25 mfurther away from your desk. At what frequencywill you hear destructive interference?A. 170 HzB. 340 HzC. 680 HzD. 1000 HzE. 1350 HzWed. Feb. 21 Phy107 Spr07 Lect 1324Interference summary• Important quantity is distance differencein number of wavelengths.• A distance difference of a half wavelengthleads to destructive interference.• Whole wavelength differenceslead to constructive interference.But destructive interference also for3 half wavelengths, 5 half-wavelengths, etc.Constructive interference also occurs at differences of2 whole wavelengths, 3 whole wavelengths5Wed. Feb. 21 Phy107 Spr07 Lect 1325Doppler Effect• A Doppler effect is experienced whenever there is relativemotion between a source of waves and an observer.• For instance, a fire engine or train passing you.– When the source and the observer are moving toward each other,the observer hears a higher frequency– When the source and the observer are moving away from eachother, the observer hears a lower frequency• Although the Doppler Effect is
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