TECH TALK


such as different technical devices or machines or different speakers, are called incoherent signals. It is nearly always justified to assume incoherent signals.


It can be shown that the relevant squared root-mean-square value (rms-value) of the total signal is the sum of the individual squared rms-values. That is, the squared rms- value of N incoherent signals is given by p2


eff=∑p2 n i=1 eff,i.


We gain the formula of level summation by expressing all N squared rms-values by their sound pressure levels Li


: Ltot=10 lg (peff/p0 =10 lg ∑10Li )2 n i=1 /10 .


This formula means that the levels are in fact not summed. Instead, the individual levels must be transformed to the squared rms- values of the sound pressures. These then add up to give the total squared rms-value - and only then can we calculate the total sound pressure level Ltot


.


For example, at a point of sound immission, there is already a sound pressure level of 50dB. How high a sound pressure level LP


can be


added, if the overall sound pressure level is not to exceed 55dB? With 10Ltot


= 10 lg (105.5


/10=105.5 −105


= 10LP /10 +105 ) =53.3 dB.


Octave and third-octave band filters Measurements of the spectral components of time domain signals are often realised using filters where the frequency range is subdivided into intervals. The filters are electronic circuits which let a supplied voltage pass only in a specific frequency band.


The filter is characterized by its lower and upper limiting frequency fl


and fu bandwidth ∆f=fu −fl , its , and its centre frequency fc


For acoustic purposes, only filters with constant relative bandwidth are used. Their bandwidth is proportional to the centre frequency of the filter. So with increasing centre frequency the bandwidth is also


. increasing. The centre frequency fc and fu of filters


with constant relative bandwidth is the geometric mean of fl


fc =√fl fu .


The octave band filter and the third-octave filter are the main filters with a constant relative bandwidth. The octave bandwidth fu


results in fc= 6


=2fl results in fc=√2fl and ∆f=fl The third-octave bandwidth fu= 3 √2fl=1.12fl and ∆f=0.26fl


.


√2fl .


form an octave band filter, since 3


√2 3 √2 3 √2=2.


The limiting frequencies are standardised in EN 60651 and EN 60652. The centre frequencies of the third-octave filters are: fc


=1.26fl Three adjacent third-octave band filters , determined by


The A-filter roughly represents the inverse of the hearing level curve with 30dB at 1kHz. The A-weighting function is standardised in EN 60651. For certain noise problems, especially for vehicle and aircraft noise, there are also less common weighting functions B, C and D. The A-weighted sound pressure level of a broader interval can again be determined by adding up appropriate third-octave or octave A-weighted levels using level summation: L(A) = 10 lg (∑10(Li


n i=1 In summary


=(1, 1.25, 1.6, 2 3.16, 4, 5, 6.3, 8)×10i The centre frequencies of the octave filters within the hearing range are 16Hz, 31, 5Hz, 63Hz, 125Hz, 250Hz, 500Hz, 1kHz, 2kHz, 4kHz, 8kHz and 16kHz.


, we can add LP


When measuring sound levels one must state which filters were used during the measurement. By using level summation, the levels of broader frequency bands may be calculated. The linear level is often given because it contains all attributes of the frequency range between 16Hz and 20kHz and can be either measured directly or determined by level summation.


Hearing levels and A-weighting The sensitivity of the human ear depends on the tonal pitch. For example, a 100Hz tone of 70dB and a 1000Hz tone of 60dB are perceived with equal loudness. The ear is more sensitive in the middle frequency range than at very high or very low frequencies.


A frequency-weighted sound pressure level is used, which accounts for the basic aspects of the human ear’s sensitivity and can also be realized with reasonable effort, the so-called A-weighted sound pressure level dB(A). This is measured using the A-filter.


Tests show that our perception is governed by relativity, where changes are perceived to be equal when the respective stimulus increases by the same percentage. The conclusion drawn is known as Weber-Fechner-Law, according to which perception is proportional to the logarithm of the stimulus.


Therefore, physical sound pressures are expressed through their logarithmic counterparts using sound pressure levels of a pseudo-unit, the decibel dB, thus mapping the sound pressure range of seven powers of ten relevant to the human ear to a scale from 0 to 140dB.


A law of level summation allows adding up sound pressure levels of incoherent signals. Filters with constant relative bandwidth, mainly octave and third-octave filters, are used to measure spectral components of a signal. A-weighting roughly captures the frequency response function of human hearing. A-weighted sound pressure levels are expressed in the pseudo- unit dB(A).


+∆i)/10 ).


26 October 2019


www.acr-news.com


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