In the previous article, we discussed L Aeq, the most widely used noise evaluation index. L Aeq is a simple and easy-to-use index that uses a frequency weighting curve (A-weighting) for pitch and energy averaging for temporal variations. As explained last time, it is widely used internationally for general environmental noise because of its good correspondence with loudness (perceived sound intensity). However, L Aeq is not a valid index that matches human perception for all sounds. This time, we will explain the masking effect and critical band, and present examples of cases where loudness and L Aeq do not correspond well, using sample sounds and data.
One common experience in daily life is the "masking effect." Conversations are difficult to hear in noisy places (for example, on a subway train) because the sounds of the subway (noise) mask the conversation (signals). Conversely, even whispering is frowned upon in quiet environments (for example, on a bus with the engine idling). To put it in slightly more technical terms, masking is the process by which the stimulus threshold for a certain sound rises due to the presence of a masking sound, and this raised threshold is called the masking threshold.
In the fourth installment of "Dimensions of Sound Analysis," we stated that "humans possess more than 20 auditory filters called critical bands, and these filters play a crucial role in distinguishing sounds." Below 500 Hz, the bandwidth of these critical bands is approximately 100 Hz, and above 500 Hz, the bandwidth is close to 1/3 octave. When noise and a signal exist simultaneously in the same critical band, the signal is easily masked by the noise, making the signal sound difficult to hear. Conversely, when they are in different critical bands, there is no masking effect, and the signal sound is easily heard. The shape of a critical band filter is a bell curve biased towards the high-frequency side. Therefore, the masking effect is greater in the region above the center frequency of the critical band and smaller in the region below it. For a detailed explanation of critical bands and masking, please refer to our website [1].
Naturally, physical quantities such as L Aeq cannot reflect these auditory characteristics. When treated physically as levels, two sounds are energetically added together, whether they are in the same critical frequency band or not. However, auditorily, if two sounds are in the same critical frequency band, the higher-pitched sound will mask the lower-pitched sound, and the loudness will not correspond to the energetically added L Aeq. For calculating loudness based on such critical frequency bands, Zwicker proposed a method for calculating loudness levels using charts, which has been standardized in ISO 532B.
Loudness level was briefly explained in the fourth column, citing literature, but to reiterate the definition in JIS Z 8106, it is "the sound pressure level of a 1,000 Hz pure tone that a person with normal hearing would perceive as being the same loudness as that sound" (quantity symbol L N, unit symbol phon). For pure tones, the loudness level can be read from the equal-loudness curve [2], but for complex tones, as shown in ISO 532B, it is determined by performing a 1/3 octave band analysis and then using a loudness chart.
So, what kinds of sounds might not correspond to L Aeq? This applies to cases where there are pure tone components in a specific frequency band. For example, if there are machine noises, the correspondence between L Aeq and loudness will deteriorate.
Here, you will listen to sound samples that are almost the same level in A-weighting but differ in loudness. The graph below shows the trends in A-weighting sound pressure level and loudness (sone)*1 for six machine sounds. The sound samples also correspond to the six machine sounds.
Thus, I believe that loudness measurements incorporating critical band and masking elements can represent a sound level that is relatively consistent with perceived loudness.
*1 Loudness (sone) and loudness level have the following relationship: Loudness is a measure of sound intensity and is a numerical value proportional to the perceived amount. Above a sound pressure level of 20 dB, a 10 dB increase doubles the loudness.
Sound Quality Evaluation 5. The Concept Behind Loudness Calculation
9-3 About time-averaged sound level
(Excerpt from the email newsletter issued on September 17, 2009)
