Relationship between Fletcher-Muson curves and Sound Level Measurements

Discussion in 'Audio Science' started by atomicbob, Dec 21, 2020.

  1. atomicbob

    atomicbob dScope Yoda

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    ISO Contours of Equal Loudness and Sound Level Measurements

    In this post I hope to shed some illumination on the ISO Contours of Equal Loudness (updated Fletcher-Munson curves) and their relationship to Sound Level Measurements.

    VERY IMPORTANT: Sound LEVEL ≠ Sound LOUDNESS

    01 iso226-2003 Equal Loudness Contours - 80 phon 100 Hz and 1000 Hz.png
    In the graph above the red lines are called equal loudness contours measured in phons. Two black lines have been added. A horizontal line at 80 dB SPL has been drawn to the 1000 Hz point on the 80 phon contour, which intersects with the 1000 Hz vertical line. Each phon line represents the necessary SPL at any given frequency to stimulate a perceived equal loudness at other frequencies.

    For the Human Auditory System (HAS) to perceive 80 phons at 100 Hz requires a stimulus of 92.5 dB SPL as shown by the blue lines, 12.5 dB higher than necessary at 1000 Hz for the same perceived loudness.



    02 iso226-2003 Equal Loudness Contours - 40 phon 100 Hz and 1000 Hz.png
    A very important characteristic about the phon lines is non-linearity. The Human Auditory System (HAS) behaves with considerably different sensitivity at 40 phons than at 80 phons for example. To achieve a similar 40 phon experience at 100 Hz requires 64 dB SPL, 24 dB higher than necessary at 1000 Hz for the same perceived loudness.


    03 ISO226 Equal Loudness Contours 94 phon.png
    1 Pascal (1 Pa) equals 94 dB SPL and is a typical reference point. Mic calibrators often operate at 1 and 10 Pa, 94 and 114 dB SPL respectively. From the 94 phon contour above it can be determined the necessary SPL to produce a 94 phon equal perceived loudness will be 126 dB SPL for 20 Hz and 102 dB for 100 Hz compared to 94 dB SPL at 1000 Hz.


    05 ISO226 Equal Loudness Contour perceived SPL 94 phon.png
    Inverting the equal loudness contour provides the relative perceived loudness when a 94 dB SPL stimulus is swept over frequency.

    A listener will experience the above perceived loudness as a sine stimulus is swept from 20 Hz to 12 KHz with calibration of 94 dB SPL at 1000 Hz, assuming an electroacoustic transducer with a flat response. Of course, such a perfect transducer doesn’t exist. Given many transducers roll off at the low end the perceived loudness will be considerably lower below 100 Hz than depicted in the line above.

    Needless to say, a sine sweep calibrated for 94 dB SPL at 1000 Hz will be most unpleasant to a listener except possibly below approximately 60 Hz.

    Now we turn our attention to Sound Level Meters and measurements. Specifically weighting curves and their relationship with Equal Loudness Contours.
    06 A-B-C weighted scales - numbers.png
    Here are the A, B and C weighting curve specifications for ANSI and ISO compliant Sound Level Meters (SLM.)


    07 SLM_A_C_curves_0_ref.png
    The graph above shows SLM A and C weighting curves. Note the A weighted curve is actually above the C weighted curve above 1000 Hz.

    A question one might ask is why these specific curves were developed.

    08 A-weight and 40 phon contour.png
    Inverting the A weighted curve and aligning with the 40 phon line a rather significant correlation is observed.


    09 B-weight and 80 phon contour.png
    Similarly a significant correlation exists between the B weighting and the 80 phon contour.


    10 C-weight and 100 phon contour.png
    Finally, a correlation exists between the 100 phon contour and C weighting.


    It would appear that SLM weighting may have had the following intended operating levels:
    11 Phon to Weight Curve intention.png

    So why would the A-weighted curve dominate measurements regardless of level?

    A-weighting can hide many low frequency issues for audio components.

    Precedence and tradition. It’s always been measured this way.

    Competition, and ignorance among customers. C-weighted measurements will likely produce higher noise levels than A-weighted. No one wants unfavorable numbers published knowing full well there are consumers who will blindly compare without understanding the underlying principles of the measurements.

    Laws tend to follow precedence as well. Long ago laws were created to hold developers accountable for residual noise in living spaces, particularly bedrooms. A-weighting is appropriate given the sound levels involved. When new laws are drafted the attorneys tend to look for precedence. A-weighted measurements proliferated. DJs and SR professionals well understand they can pump the bass and stay legal given the inappropriate use of A-weighting as required by ordinances everywhere. C-weighting would be disastrous for the venue while a welcome relief for the neighbors.

    Finally OSHA standards were a compromise. NIOSH standards are much more stringent and better aligned with actual hearing noise exposure risks. The researcher upon whose work OSHA standards are based has inferred to colleagues the standards should be updated to reflect lowering of the acceptable levels over time by approximately 10 dB.

    20201223 edited for clarity, 1st and 2nd graphs updated with better visual information.
     
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    Last edited: Dec 23, 2020
  2. Hammy

    Hammy Friend

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    The Dangerous Decibels web site needs to explain safe bass listening dB levels the way you just did. Along with your explanation in another thread about how loud bass levels can vibrate the high frequency cilia like seaweed in a tsunami and can cause hearing damage to higher frequency hearing.
     
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  3. atomicbob

    atomicbob dScope Yoda

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    The first post has been edited for clarity and with better visualizations for first and second graphs.

    Below is a comparison of NIOSH and OSHA standard.
    NIOSH-OSHA-Standards.png
    While it would appear that 94 dB SPL is safe for an hour according to NIOSH, what isn't stated explicitly here is the need for the cilia and basilar membrane to rest the remainder of a 24 hr period, preferably in a very quiet ambient environment. Additionally the sound levels assume some distribution to the noise spectrum, not a single frequency. Listen to an 85 80 dB SPL 1 KHz tone for 30 seconds and then stop. The listener's auditory system now has a threshold shift at that frequency. Upon removal of the stimulus the listener will experience the equivalent of a notch at 1 KHz until the threshold shift returns to normal.

    Loosely similar to lifting weights. If the load is light one may perform many repetitions. But if the load is heavy fewer repetitions will be tolerable before requiring rest. Then the lifter must rest for a long period before the next exercise period.

    Don't take your hearing for granted.
    Once permanent hearing loss has occurred it is for the remainder of your life.


    20201223 edited to change 85 dB to 80 dB for 1 KHz tone experiment based on conversation with an old Bell Labs researcher who has more data than I.
     
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    Last edited: Dec 23, 2020
  4. Psalmanazar

    Psalmanazar Most improved member; A+

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    Most musicians and audio professionals have permanent hearing damage. The ones that don't are mostly lying. That's part of the business. Classical musicians often think they're an exception but usually they're some of the deafest ime due to sitting in massive sea of volume almost every night for years. Guitarists can't get that type of exposure from a practice amp.

    I've never heard of anyone willingly blasting anything to the point of audible distortion like Amir. It's usually poorly isolated headphones cranked up, feedback nightmares, pops, noise bursts, or just gradual hearing loss.
     
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