# frequencies - PowerPoint

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```					  FREQUENCY SPECTRUM OF A
SOUND

A sound which consists of a single frequency
is called a pure tone
Sound with various frequencies

Noise produced by most mechanical sources,
such as machines, is made up of many different
unrelated frequencies (wide band noise), and
tends to sound unpleasant.
The graph of the
magnitude of the
sound pressure
level at each
frequency      is
called       the
frequency
spectrum of the
sound.
FREQUENCY ANALYSIS

It is often necessary to obtain
spectrum of a sound to design effective
noise control and to select appropriate
personal hearing protectors
OCTAVE BANDS
• In most cases it is sufficient to measure the
sound pressure level in bands of frequencies,
rather than at individual frequencies.
•The width of the band usually chosen is the
octave band - this is a band where the upper
frequency is twice that of the lower.
•Each band is denoted by its centre
frequency. Those usually measured are the
Internationally Preferred Frequencies of:
31.5   63   125   250   500   1k   2k   4k   8k   16k
Hz    Hz   Hz    Hz    Hz    Hz   Hz   Hz   Hz   Hz
This is a typical spectrum of a circular saw cutting
aluminium
The limits of the octave bands are shown in
the Table below
Centre frequency, Hz   Limits of band, Hz
31.5                22 - 45
63                 45 - 89
125                89 - 177
250                177 - 353
500                353 - 707
1000               707 - 1414
2000              1414 - 2828
4000              2828 - 5657
8000              5657 - 11314
16000             11314 - 22627
Note that the centre frequency is the geometric
mean and not the average of the band limit
frequencies.
The lower and upper frequencies in the band
can be found from the centre frequency by:

f lower=
=

f upper=fcentrex 2 =1.414
ONE-THIRD OCTAVE BANDS
Sometimes we want more detailed
information than the octave band analysis
will give. This can be provided by selecting
narrower bands, such as one-third octave
bands.

One-third octave band centre frequencies in
the audible range are:
25, 31.5, 40, 50, 63, 80, 100, 125, 160, 200,
250, 315, 400, 500, 630, 800, 1k, 1.25k,
1.6k, 2k, 2.5k, 3.15k, 4k, 5k, 6.3k, 8k, 10k,
12.5k, 16k, 20k Hz.
The lower and upper frequencies of the
one-third octave bands are given by:
flower =

fupper = fcentre x 21/6 = 1.122 x fcentre
NARROW BAND ANALYSIS
For even more detailed examination,
narrow band analysis is possible. This is
used to pick up tonal noises with very
narrow frequency bandwidths which would
be missed by octave or one-third octave
band analysis.
FREQUENCY WEIGHTING NETWORKS
A AND C WEIGHTING NETWORKS
• Since the ear does not have an equal response to
sounds of different frequencies we need to take this
into account when we measure sound in relation to
its effect on people.
CENTRE FREQUENCIES
From the weighting curves above, you can see that
the following are the adjustments at octave band
centre frequencies:

31.   63    125   250   500   1000   2000   4000   8000   16000
Octave Band Centre
5
Frequencies, Hz

-39   -26   -16   -9    -3     0     +1     +1      -1     -7
A-weighting

-3    -1    0     0     0      0      0      -1     -3     -8
C-weighting
Example: What is the A-weighted sound
pressure level in the cab of a diesel
locomotive where the following octave band
sound pressure levels were measured?

31.        12   25   50   100   200   400   800   1600
63
5          5    0    0    0     0     0     0      0
Octave Band Centre Frequencies, Hz

10    10
92   90   87   82    80    68    60    57
Diesel locomotive octave band         4     2
levels, dB

-    -
-39             -9   -3   0     +1    +1    -1     -7
26   16

A-weighted octave band levels,
65    76   76   81   84   82    81    69    59    50
dB(A)

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