Sound Model Report
Introduction
When an
object vibrates in matter, it produces sound.
In this project however, we are mostly interested in the travel of sound
through air. Sound is defined as a
pressure variation in a medium which a human ear can detect. When something
vibrates in the atmosphere, it moves the air particles around it. Those
particles in turn move the air particles around them, carrying the pulse of
pressure variation through the air.
Humans can pick up theses pressure variations and interpret them as what
we know to be sound. The human ear can
process sound at frequencies from 20 to 16,000 Hz. The frequency of the sound refers to the
number of pressure changes per second.
Lower frequencies can be physically felt instead of heard, but higher
frequencies cannot be perceived at all.
A
very important property to know about sound is its wavelength. The wavelength of a sound can be found if the
speed and the frequency of the sound are known.
The wavelength is the ratio of distance traveled to the time it takes to
complete one cycle. In an industrial
situation, the wavelength is a key factor to know when faced with the task of
sound reduction. Environmental acoustic
engineers seem to focus their acoustic design on the sound frequency range of
44 – 11,300 Hz.
This frequency range of 44
– 11,300 Hz is broken down in to eight sections called octave bands. Each octave band covers a specific range of
frequencies and excludes all others.
Each octave band has an upper and lower cutoff frequency along with a
center frequency. The eight bands have
center frequencies of: 63,
125, 250, 500, 1000, 2000, 4000 and 8000 Hz.
These eight octave bands are broken down into even smaller 1/3 octave
bands for an even smaller frequency range to analyze.
In
the case of the snowmobile, we have a steady noise with audible discrete tones.
This is called discrete frequency noise and
is the most common noise found in industry. This type of noise has the
characteristic of pure tones over a number of frequencies. Discrete frequency
noise is caused by rotating parts of machines such as fans, internal combustion
engines, transformers and pumps.
For
our purposes in sound analysis and reduction of noise on the snowmobile, we
need to focus on different areas of the sled, and then locate the sources of
noise. Methods to reduce the noise
consist of the application of sound dampening materials, quieter drive train
and exhaust components, and an optimum sound reducing cowl shape. These modifications will allow us to change
the frequency range to a value that will be perceived as the quietest on an
A-weighted scale.
A
possible problem that will be encountered in the design of sound reduction
components is the fact that sounds at lower frequencies have a substantially larger
wavelength than those sounds at a higher frequency. These long wavelengths allow the sound to
more easily pass around bends or through certain materials. This will have to be accounted for when
designing around components that produce low frequency sound.
To
monitor the sound coming from the sled, we can use the spectral analyzer to
gather sound though the frequency band.
Although it is possible to analyze a source on a frequency by frequency
basis, it is both impractical and time consuming. With this in mind, the process can easily be
simplified by plotting frequency ranges on a logarithmic scale. By use of the convolution integral,
frequencies can be broken down into 1/3 octaves. Sound measured in a particular octave band is
the logarithmic sum of the sound at each of the band’s frequencies: dB = 10 log 10(N / NREF)
Sound Pressure Level (SPL) and Sound Power Level (PWL)
Sound
pressure level is the change in air pressure above and below the average
atmospheric pressure whose
intensity is influenced not only by the strength of the source, but also by the
surroundings and the distance from the source to the receiver. These pressure changes can be very
significant. To measure these wide
changes in amplitude, sound pressure is converted into decibels,
and referred to as the Sound Pressure Level (SPL). This scale begins at zero decibels and the
international standard of pressure change of 2 x 10 –5 Pa.
SPL := 20⋅Log10⋅P + 94
P =
root mean square sound pressure in Pa.
The
sound pressure level can be measured simply by a sound meter anywhere, the
sound power level must be determined in an acoustics laboratory, usually by the
manufacturer of a component. Since the
only accurate measurement a manufacturer can provide is the sound power level,
in our design for sound reduction, we must take into account environmental
factors.
A-Weighted Scale
The human ear
does not perceive all frequencies of sound with the same intensity. Very low and very high frequencies are not
heard while sound with frequencies between 2000 and 5000 Hz is heard much more
clearly.
An A-Weighted
Scale adjusts the sound level to conform to the frequency response of the human
ear. This allows a sound level meter to
have the same sensitivity as the human ear.
The meter using an A – Weighted Scale assigns a weighting of 0 to sounds
with frequencies of 10 cycles per second or less and assigns maximum weighting
to sounds with frequencies of 2000-5000 cycles per second. In this way, the sound level meter will
display the sound level in dB(A), and will reflect more accurately the sound as
heard by the human ear.
Far Field Effect
The Far-Field
Effect describes how sound behaves as it moves away from a source. In the far-field, the sound waves created by
the source are in phase. The size of the
source determines where the far-field starts, but when in the far-field, the
sound level decreases approximately 6 dB for every doubling of distance.
The
importance of the far-field effect for this project is the fact that to
reliably measure sound level, the meter must be located in the far-field. Once in the far-field, the frequency response
of a source will be approximately the same with changing distance. If the sound level meter is located closer to
the source than the boundary of the far-field, the frequencies will change
along with the sound level, resulting in unreliable data.
Sound
Absorbing Materials
Sound
absorbing materials are porous materials used to reduce sound by
absorption. The effectiveness is
dependant on many factors including thickness, density and porosity. For every inch of thickness, the sound loss
is about 1 dB at 100 Hz and about 4 dB at 3000 Hz. When talking about sound, there is absorption
and insulation. Absorption refers to the
amount of sound that is reflected and insulation refers to the amount of sound
that is allowed to pass through the material.
A lead sheet has high insulation but practically no absorption, meaning
that virtually no sound is allowed to pass through the surface but there is high
reflection off the surface of the sheet.
The absorption coefficient (α) is the amount of sound absorbed at
the materials surface. The higher the
absorption coefficient the better the sound is absorbed. This number can range from 0.01 (almost no
absorption – all reflected) to 1.0 (total absorption – no reflection). The absorption coefficient increases as the
frequency of a noise increases. At lower
frequencies, the material must be thicker in order to absorb the sound. The performance of a sound absorbing material
is usually described using the noise reduction coefficient (NRC). The NRC is the average of the absorption
coefficient at 250, 500, 1000 and 2000 Hz.
Damping
Materials
Damping
materials are materials that are used to reduce structure borne noise. Structure borne noise comes from mechanical
vibrations that are transferred from the machinery to the surrounding
structure. An example would be a piece
of machinery that is bolted to a concrete floor. A large amount of vibrations are carried from
the machine to the floor which results in a large amount of structural
noise. A damping material could be
placed between the machinery and the floor to absorb some of the vibration
energy. Damping materials convert the
vibration energy to heat energy through friction. An example of a damping material would be a
high density sandwiched between low density materials. The energy is transferred to the high density
mid layer and the low density materials on the outside allow the mid layer to
vibrate thus producing heat and reducing sound.
Transmission Loss or Barrier Materials
Good
barrier materials are dense and rigid and are defined in terms of their
Transmission Loss (TL), for instance steel is better than plywood. Transmission
Loss is defined as the logarithmic ratio of the power of sound on one side of a
barrier to the power of sound transmitted to the other side. As the density and
frequency of the barrier increases as does the (TL). The higher the TL, the
better a barrier material is at limiting or attenuating the amount of sound and
vibration traveling through it. For example, a wall or barrier having a TL of
50 dB reduces a 110 dB interior noise level to 60 dB. A wall with a TL of 30 dB
reduces the same amount of noise to 80 dB. TL is calculated using the following
equation:
TL (dB) = 10 log 1/t = 10 log Wi/Wt
ô = sound transmission coefficient;
The ratio of the PWL incident on one side to PWL on the other side
Wi = incident sound power (PWL on source side)
Wt = transmitted sound power (PWL on the receiver side)
PWL
can easily be calculated from SPL
Convolution Integral
The
noise level measured on the outside of the cowling can be treated as a
convolution integral of the following form:
Variables:
X
is the noise from the engine and clutch assembly
H
is the response of the entire cowl on the sled
Each
value at each 1/3-octave band is just multiplied.
The
convolution integral provide the noise level outside of the cowling,
Y, in relationship with the time, T.
With the value for noise level on the outside of the cowling known from the
convolution integral we can select the best material from our material matrix
to reduce snowmobile noise.