Sound Physics 123 9172020 Lecture IV 1 Sound

Sound Physics 123 9/17/2020 Lecture IV 1

Sound • Wave nature of sound • Intensity of sound • Standing sound waves – String instruments – Pipes • Interference and beats. • Doppler effect 9/17/2020 Lecture IV 2

Sound = longitudinal wave in air 9/17/2020 Lecture IV 3

Speed of sound • Wave characteristics: – Wave length – l (m) – Frequency – f(Hz) - pitch – Wave velocity - v=l f, m/s • Wave speed – property of material one – to – one correspondence of frequency and wave length in a given medium: 9/17/2020 Lecture IV 4

Intensity of sound • Intensity of sound: I=10 -12 102 W/m 2 – 14 orders of magnitude • Measure of loudness b in Decibel: b(in d. B)=10 log (I/I 0) 9/17/2020 Lecture IV I 0 5

Sensitivity of human ear Audible range (really good speakers) : 20 Hz – 20 k. Hz 9/17/2020 Lecture IV 6

Physics of a guitar • Guitar = strings + sounding box (resonator) • Strings force resonance in the sounding box • Fundamental frequency • Strings • Tuning 9/17/2020 Lecture IV 7

Physics of a guitar • Standing wave • Fundamental frequency: – L=l 1 /2 l 1=2 L – f 1=v/l 1 f 1=v /(2 L) 9/17/2020 Lecture IV String theory: Thicker string higher m/l lower v lower frequency f Tuning: Increase tension (FT) increase v increase frequency f. Fingered string: Decrease L decrease l increase f. 8

Wave velocity vs particle velocity • • w=2 pf – cyclic frequency, k=2 p/l –wave vector D=D 0 sin(kx-wt) Riding the wave kx-wt=const kx-wt=c x=c/k+(w/k)t = x 0+vt Thus, wave velocity v=w/k=2 pf/ (2 p/l)=fl = l/T D=D 0 sin(kx-wt) medium displacement at point x at time t Particle velocity: – vp=d. D/dt=-w. D 0 cos(kx-wt)=-vmaxcos(kx-wt) – vmax=w. D 0 9/17/2020 Lecture IV 9

Physics 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): Dx = max • Pressure = Atmospheric P: DP=0 • Closed end (pushed against a wall) • Displacement Dx = 0 • Pressure variation – max DP=max 9/17/2020 Lecture IV 10

Organ pipe 9/17/2020 Lecture IV 11

Organ pipe 9/17/2020 Lecture IV 12

Interference Two waves of the same frequency C: Constructive interference A+A=2 A I =4 I 0 Dx=0+nl; dsinq=nl D: Destructive interference A-A=0 I =0 Dx=l/2+nl dsinq=(n+1/2)l 9/17/2020 Lecture IV 13

Beats Two waves of the similar frequencies: f 1 and f 2. 9/17/2020 Lecture IV 14

Doppler effect • • sound source moving with velocity vs Distance between crests l’=l-vs. T=l-vsl/v=l(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 pitch 9/17/2020 Lecture IV 15

Demo data • Open-closed end pipe • f=512 Hz • v=343 m/s (maybe less, cold) • l=v/f=. 67 m • l=4 l 1 • l 1=l/4=0. 17 m • l 3=3 l/4=0. 51 m 9/17/2020 Lecture IV 16

Intensity of waves • Energy of oscillation E is proportional to amplitude squared A 2 • Intensity – I, W/m 2 • Intensity I is proportional to amplitude squared A 2, inversely proportional to r 2: 9/17/2020 Lecture IV 17