1

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