Physics 123

1
Sound

• Physics 123

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Sound

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

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Sound longitudinal wave in air
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Speed of sound

• Wave characteristics
• Wave length l (m)
• Frequency f(Hz) - pitch
• Wave velocity - vl 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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Intensity of sound

• Intensity of sound I10-12 ? 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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Sensitivity of human ear
Audible range (really good speakers) 20Hz 20
kHz
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Physics of a guitar

• Guitar strings sounding box (resonator)
• Strings force resonance in the sounding box
• Fundamental frequency
• Strings
• Tuning

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Physics of a guitar
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
• Ll1 /2 l12L
• f1v/l1 f1v /(2L)

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Wave velocity vs particle velocity

• w2pf cyclic frequency, k2p/l wave vector
• DD0sin(kx-wt)
• Riding the wave kx-wtconst
• kx-wtc xc/k(w/k)t x0vt
• Thus, wave velocity vw/k2pf/ (2p/l)fl l/T
• DD0sin(kx-wt) medium displacement at point x at
  time t
• Particle velocity
• vpdD/dt-wD0cos(kx-wt)-vmaxcos(kx-wt)
• vmaxwD0

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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
• DP0
• Closed end (pushed against a wall)
• Displacement
• Dx 0
• Pressure variation max
• DPmax

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Organ pipe
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Organ pipe
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Interference
C Constructive interference AA2A ? I
4I0 Dx0nl dsinqnl
Two waves of the same frequency
D Destructive interference A-A0 ? I
0 Dxl/2nl dsinq(n1/2)l
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Beats
Two waves of the similar frequencies f1 and f2.
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Doppler effect

• sound source moving with velocity vs
• Distance between crests ll-vsTl-vsl/vl(1-vs/v)
  
• Frequency ff/(1-vs/v)
• Moving towards you vs positive ? divide by a
  number lt1 ? fgtf higher pitch
• Moving away from you vs negative ? divide by a
  number gt1 ? fltf lower pitch

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Demo data

• Open-closed end pipe
• f512 Hz
• v343m/s (maybe less, cold)
• lv/f.67m
• l4l1
• l1l/40.17m
• l33l/40.51m

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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