Design and Simulation of Two Stroke Engines

Chapter 8 • Reduction of Noise Emission from Two-Stroke Engines
texts [1.8], but as this word is most meaningful to you, and to any listener, as a way to express
perceived noise level as measured by pressure, I feel justified in using it in that context within
this text.
The relationship between intensity and loudness is fixed for sounds which have a pure
tone, or pitch, i.e., the sound is composed of sinusoidal pressure waves of a given frequency.
For real sounds that relationship is more complex. The intensity of the sound, being an energy
value, is denoted by units of W/m 2 . Noise meters, being basically pressure transducers, record
the "effective sound pressure level," which is the root-mean-square of the pressure fluctuation
about the mean pressure caused by the sound pressure waves. This rms pressure fluctuation
is denoted by dp, and in a medium with a density, p, and a reference speed of sound, ao,
the intensity is related to the square of the rms sound pressure level by:
I = dy
pa0
(8.1.2)
The pressure rise, dp, can be visually observed in Plates 2.1-2.3 as it propagates away
from the end of an exhaust pipe.
The level of intensity that can be recorded by the human ear is considerable, ranging from
1 pW/m 2 to 1 W/m 2 . The human eardrum, our personal pressure transducer, will oscillate
from an imperceptible level at the minimum intensity level up to about 0.01 mm at the highest
level when a sensation of pain is produced by the nervous system as a warning of impending
damage. To simplify this wide variation in physical sensation, a logarithmic scale is used to
denote loudness, and the scale is in units called a Bel, the symbol for which is B. Even this
unit is too large for general use, so it is divided into ten subdivisions called decibels, the
nomenclature for which is dB. The loudness of a sound is denoted by comparing its intensity
level on this logarithmic scale to the "threshold of hearing," which is at an intensity, Io, of 1.0
pW/m 2 or a rms pressure fluctuation, dpo, of 0.00002 Pa, which is 0.0002 ubar. Thus, intensity
level of a sound, III where the actual intensity is 11, is given by:
J L1 = lQ gl0 *V
\ 1 0J
B
(-, \
101og10
v T oy dB
(8.1.3)
In a corresponding fashion, a sound pressure level, Pi, where the actual rms pressure
fluctuation is dpi, is given by:
Pi = lo gl0 V
Jo)
543
B