Understanding Sound Physics: Waves, Intensity, Instruments & Effects

1. Sound Physics 123 Lecture IV

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

3. Sound = longitudinal wave in air Lecture IV

4. 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: Lecture IV

5. Intensity of sound • Intensity of sound: I=10-12 102 W/m2 – 14 orders of magnitude • Measure of loudness bin Decibel: b(in dB)=10 log (I/I0) I0 Lecture IV

6. Sensitivity of human ear Audible range (really good speakers) : 20Hz – 20 kHz Lecture IV

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

8. Physics of a guitar • Standing wave • Fundamental frequency: • L=l1 /2 l1=2L • f1=v/l1 f1=v /(2L) 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. Lecture IV

9. Wave velocity vs particle velocity • w=2pf – cyclic frequency, k=2p/l –wave vector • D=D0sin(kx-wt) • Riding the wave kx-wt=const • kx-wt=c x=c/k+(w/k)t = x0+vt • Thus, wave velocity v=w/k=2pf/ (2p/l)=fl = l/T • D=D0sin(kx-wt) medium displacement at point x at time t • Particle velocity: • vp=dD/dt=-wD0cos(kx-wt)=-vmaxcos(kx-wt) • vmax=wD0 Lecture IV

10. 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 Lecture IV

11. Organ pipe Lecture IV

12. Organ pipe Lecture IV

13. Interference C: Constructive interference A+A=2A  I =4I0 Dx=0+nl; dsinq=nl Two waves of the same frequency D: Destructive interference A-A=0  I =0 Dx=l/2+nl dsinq=(n+1/2)l Lecture IV

14. Beats Two waves of the similar frequencies: f1 and f2. Lecture IV

15. Doppler effect • sound source moving with velocity vs • Distance between crests l’=l-vsT=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 Lecture IV

16. Open-closed end pipe f=512 Hz v=343m/s (maybe less, cold) l=v/f=.67m l=4l1 l1=l/4=0.17m l3=3l/4=0.51m Demo data Lecture IV

17. Intensity of waves • Energy of oscillation E is proportional to amplitude squared A2 • Intensity – I, W/m2 • Intensity I is proportional to amplitude squared A2, inversely proportional tor2: Lecture IV