week 7 - cas.miamioh.edu › ~jaegerh › phy131 › week07-tu.pdf · spring 2007 – week 7 phy...
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Spring 2007 – Week 7 PHY 131 1
Week 7
• Sound Level of Multiple Sources
• Loudness Level and Loudness
• Loudness of Pure and Complex Tones
• Loudness and Masking of Sound
Spring 2007 – Week 7 PHY 131 2
Sound intensity is related to sound pressure: p2 = I Zo
Zo is called the characteristic impedance of the medium and isconstant for a given medium (e.g. air) as long as the temperatureand the air pressure remain the same.
Sound Pressure Level
SPL = 20 log p1p2
⎛⎝⎜
⎞⎠⎟
p12
p22 =
I1Zo
I2Zo
=I1I2
p12 = I1Zo and p2
2 = I2Zo
SIL = 10 log I1I2
⎛⎝⎜
⎞⎠⎟= 10 log p1
2
p22
⎛⎝⎜
⎞⎠⎟= 20 log p1
p2⎛⎝⎜
⎞⎠⎟
2
Spring 2007 – Week 7 PHY 131 3
Sound Intensity and Pressure Level
SPL = 20 log ppo
⎛⎝⎜
⎞⎠⎟
po = 2 ×10−5Pa
SIL = 10 log II0
⎛⎝⎜
⎞⎠⎟
Io = 10−12 Wm2
Spring 2007 – Week 7 PHY 131 4
SIL of N Equal Intense Sources
SIL(1) = 10 log II0
⎛⎝⎜
⎞⎠⎟
SIL(2) = 10 log 2 × II0
⎛⎝⎜
⎞⎠⎟= 10 log( I
I0) +10 log2 = SIL(1) + 3dB
SIL(N ) = 10 log N × II0
⎛⎝⎜
⎞⎠⎟= 10 log( I
I0) +10 logN = SIL(1) +10 logN
3
Spring 2007 – Week 7 PHY 131 5
SIL of Not Equal Sources
SIL(1) = 70 dB SIL(2) = 76 dB
70 = 10 log I1I0
⎛⎝⎜
⎞⎠⎟
7 = log I1I0
⎛⎝⎜
⎞⎠⎟
I1 = 107 × Io
76 = 10 log I2I0
⎛⎝⎜
⎞⎠⎟
7.6 = log I2I0
⎛⎝⎜
⎞⎠⎟
I2 = 107.6 × Io = 4 ×10
7 × Io
Spring 2007 – Week 7 PHY 131 6
SIL of Not Equal Sources
SIL(1+ 2) = 10 log 5 ×107 × IoI0
⎛⎝⎜
⎞⎠⎟= 10 log 5 ×107( )
I1 = 107 × Io I2 = 4 ×10
7 × Io
I = I1 + I2 = 1×107 × Io + 4 ×107 × Io = 5 ×107 × Io
SIL(1+ 2) = 10 log 5( ) + 10 log 107( ) = 7 + 70 = 77 dB
70 dB 76 dB
4
Spring 2007 – Week 7 PHY 131 7
SIL of Not Equal Sources
SIL(1) = 70 dB SIL(2) = 90 dB
70 = 10 log I1I0
⎛⎝⎜
⎞⎠⎟
7 = log I1I0
⎛⎝⎜
⎞⎠⎟
I1 = 107 × Io
90 = 10 log I2I0
⎛⎝⎜
⎞⎠⎟
9 = log I2I0
⎛⎝⎜
⎞⎠⎟
I2 = 109 × Io
Spring 2007 – Week 7 PHY 131 8
SIL of Not Equal Sources
SIL(1+ 2) = 10 log 1.01×109 × IoI0
⎛⎝⎜
⎞⎠⎟= 10 log 1.01×109( )
I1 = 107 × Io I2 = 10
9 × Io
I = I1 + I2 = 1×107 × Io + 109 × Io = 1.01×109 × Io
SIL(1+ 2) = 10 log 1.01( ) + 10 log 109( ) = 0 + 90 = 90 dB
70 dB 90 dB