1. Sound
Physics 123
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2. Sound Wave nature of sound Intensity of sound Standing sound waves
String instruments
Pipes
Interference and beats.
Doppler effect
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3. Sound = longitudinal wave in air
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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:
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5. Intensity of sound
Intensity of sound: I=10-12  102 W/m2 – 14 orders of magnitude
Measure of loudness b in Decibel: b(in dB)=10 log (I/I0) I0
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6. Sensitivity of human ear
Audible range (really good speakers) : 20Hz – 20 kHz
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7. Physics of a guitar Guitar = strings + sounding box (resonator)
Strings force resonance in the sounding box
Fundamental frequency
Strings
Tuning
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8. Physics of a guitar Standing wave Fundamental frequency: L=l1 /2 l1=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.
Standing wave
Fundamental frequency:
L=l1 /2 l1=2L
f1=v/l f1=v /(2L)
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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
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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
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11. Organ pipe
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12. Organ pipe
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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
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14. Beats Two waves of the similar frequencies: f1 and f2. 11/16/2018
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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
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16. Demo data 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
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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 to r2:
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