Audio Engineering

70 Chapter 2

o r

D

cm f

LP

   

^

39 10

3 0 0002.^1010

⎛

⎝

⎜⎜

⎜⎜

⎜

⎞

⎠

⎟⎟

⎟⎟

⎟⎟

(2.48)

where Din is the displacement in inches (the rms amplitude) of the air, Dcm is the
displacement in centimeters,f is the frequency in hertz, and LP is the sound level in
decibels referred to 0.00002 N/m^2.

Example
What is the displacement of the eardrum in inches for a tone at 1000 Hz at a level of
74 dB? Using Eq. (2-51),

Din    



310 ^10

1000

0 0000015

7

⎛^7420

⎝

⎜⎜

⎜⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎟

.in

which is a displacement of approximately one-one-millionth of an inch (0.000001 in).

2.22 The Phon ..................................................................................................................

Figure 2.17 shows free-fi eld equal-loudness contours for pure tones (observer facing
source), determined by Robinson and Dadson at the National Physical Laboratory,
Teddington, England, in 1956 (ISO/R226-1961). The phon scale is of equal-loudness
level contours. At 1000 Hz every decibel is the equivalent loudness of a phon unit.

For two different sounds within a critical band (for most practical purposes, using^1 ⁄ 3
octave bands suffi ces) they are added in the same manner as decibel readings.

PT

Lp Lp





10 10 10

1

10

2

log⎛^10

⎝

⎜⎜⎜ ⎞

⎠

⎟⎟

⎟

phons (2.49)

where LP 1 and LP 2 are the individual sound levels in dB.