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 information about the frequency 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 Hz

63 Hz

125 Hz

250 Hz

500 Hz

1k Hz

2k Hz

4k Hz

8k Hz

16k 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, Hz31.5 22 - 4563 45 - 89

125 89 - 177250 177 - 353500 353 - 707

1000 707 - 14142000 1414 - 28284000 2828 - 56578000 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.

                                                                                                                        

          

ADJUSTMENTS AT OCTAVE BAND CENTRE FREQUENCIES

From the weighting curves above, you can see that the following are the adjustments at octave band centre frequencies:

Octave Band Centre Frequencies, Hz

31.5

63   125 250 500 1000 2000 4000 8000 16000

                                                                                                                                                                 

A-weighting adjustment, dB

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

C-weighting adjustment, dB

-3 -1 0 0 0 0 0 -1 -3 -8

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?

Octave Band Centre Frequencies, Hz

31.5

63125

250

500

1000

2000

4000

8000

16000

                                                                                                                                                                                   

Diesel locomotive octave band levels, dB

104

102

92 90 87 82 80 68 60 57

A-weighting adjustment -39

-26

-16

-9 -3 0 +1 +1 -1 -7

A-weighted octave band levels, dB(A)

65 76 76 81 84 82 81 69 59 50