SoundSlide 2Sound = longitudinal wave in airSpeed of soundIntensity of soundSensitivity of human earPhysics of a guitarSlide 8Wave velocity vs particle velocityPhysics of an organOrgan pipeSlide 12InterferenceBeatsDoppler effectDemo dataIntensity of waves01/14/19 Lecture IV 1Physics 123Sound01/14/19 Lecture IV 2Sound•Wave nature of sound•Intensity of sound•Standing sound waves–String instruments–Pipes•Interference and beats.•Doppler effect01/14/19 Lecture IV 3Sound = longitudinal wave in air01/14/19 Lecture IV 4•Wave characteristics:–Wave length – (m)–Frequency – f(Hz) - pitch–Wave velocity - v= f, m/s•Wave speed – property of material one – to – one correspondence of frequency and wave length in a given medium: Speed of soundvf 01/14/19 Lecture IV 5•Intensity of sound: I=10-12 102 W/m2 – 14 orders of magnitude•Measure of loudness in Decibel: (in dB)=10 log (I/I0)Intensity of soundI001/14/19 Lecture IV 6Sensitivity of human earAudible range (really good speakers) : 20Hz – 20 kHz01/14/19 Lecture IV 7•Guitar = strings + sounding box (resonator) •Strings force resonance in the sounding box•Fundamental frequency•Strings•TuningPhysics of a guitar01/14/19 Lecture IV 8•Standing wave•Fundamental frequency: –L=/21=2L–f1=v/1 f1=v /(2L)Physics of a guitarlmFvT/lengthunit per mass tensionstringString theory:Thicker string higher m/l lower v lower frequency fTuning:Increase tension (FT) increase v increase frequency f.Fingered string:Decrease L decrease increase f.01/14/19 Lecture IV 9Wave velocity vs particle velocity f – cyclic frequency, k=2–wave vector•D=D0sin(kx-t)•Riding the wave kx-tconst•kx-t=c x=c/k+(kt = x0+vt•Thus, wave velocity v=k=f/ (2f•D=D0sin(kx-t) medium displacement at point x at time t•Particle velocity:–vp=dD/dt=-D0cos(kx-t)=-vmaxcos(kx-t)–vmax=D001/14/19 Lecture IV 10Physics of an organ•Open and closed pipes - resonators •Boundary conditions (imagine yourself in a crowded room) :•Open end (next to an open door)•Displacement (freedom to move):x = max•Pressure = Atmospheric P:P=0 •Closed end (pushed against a wall)•Displacement x = 0 •Pressure variation – maxP=max01/14/19 Lecture IV 11Organ pipe0 max; Px1nffn01/14/19 Lecture IV 12max ;0 Px112)12(:harmonics oddonly fnfnOrgan pipe01/14/19 Lecture IV 13InterferenceC: Constructive interferenceA+A=2A I =4I0x=0+ndsinnD: Destructive interferenceA-A=0 I =0x=/2+ndsin=(n+1/2)Two waves of the same frequency01/14/19 Lecture IV 14BeatsTwo waves of the similar frequencies: f1 and f2.01/14/19 Lecture IV 15Doppler effect•sound source moving with velocity vs•Distance between crests ’=-vsT=l-vs/v=(1-vs/v)•Frequency f’=f/(1-vs/v)•Moving towards you vs – positive divide by a number <1 f’>f – higher pitch•Moving away from you vs – negative divide by a number >1 f’<f – lower pitch01/14/19 Lecture IV 16Demo data•Open-closed end pipe•f=512 Hz•v=343m/s (maybe less, cold)• =v/f=.67m=4l1 •l1=/4=0.17m• l3=3/4=0.51m01/14/19 Lecture IV 17Intensity of wavesrA1•Intensity – I, W/m2•Intensity I is proportional to amplitude squared A2, inversely proportional to r2:•Energy of oscillation E is proportional to amplitude squared A22AE areapowerareatimeenergyI /2AI 21rI
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