{"id":8896,"date":"2026-06-16T09:09:42","date_gmt":"2026-06-16T07:09:42","guid":{"rendered":"https:\/\/www.tonmeister.ca\/wordpress\/?p=8896"},"modified":"2026-06-16T09:28:20","modified_gmt":"2026-06-16T07:28:20","slug":"pet-peeve-of-a-pedant","status":"publish","type":"post","link":"https:\/\/www.tonmeister.ca\/wordpress\/2026\/06\/16\/pet-peeve-of-a-pedant\/","title":{"rendered":"Pet Peeve of a Pedant"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Once-upon-a-time, I taught a course in electroacoustic measurements at McGill. I used to devote an entire 3-hour class to explaining decibels, partly because we use them so often in audio, partly because I had such difficulty wrapping my own head around them when I was starting off, and partly because the reason I and many other people have that problem is largely due to the laziness of others.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Yesterday, I found myself being annoyed once again by this laziness as I edited a scan of a document from 1961 to correct it before posting it online&#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Some background information:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We humans generally respond to things logarithmically. Without getting into the math, this means that our reptile brains like multiplication more than addition. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example: if I have $10 in the bank, and you have $100 &#8211; and we both win $10 in a lottery, I&#8217;ll be happier than you. We both won the same amount of money, but I won 100% of my current balance, whereas you only won 10% of your current balance.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Another example is a piano keyboard. Each octave looks the same distance on the keyboard, but the fundamental frequency of those notes are doubling each time you go up one octave. So, a piano keyboard (and music notation) are frequencies displayed on a logarithmic scale.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is also true of detecting how loud things are: we think &#8220;twice as loud&#8221; or &#8220;half as loud&#8221; when talking about the Sound Pressure Level (SPL) that we hear.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We use percent and octaves to do two things:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first is to convert the values we&#8217;re talking about into multiplications instead of additions.<\/li>\n\n\n\n<li>The second is to compare a value (like our lottery winning) to another value (like the bank account balance). (It wouldn&#8217;t make sense if I said &#8220;I bought a lottery ticket and I won 100%!&#8221; 100 percent of what?)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">When it comes to comparing levels of things like Sound Pressure Level, electrical power, voltages, or radio signal power, we use decibels (or dB) to make the scale logarithmic.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, you&#8217;ll see someone write something like &#8220;the sound of a jet engine at takeoff is 120 decibels&#8221;, which is when my pet peeve rears its ugly head. The problem is that this sentence is incomplete. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you do the math, then you find out that &#8220;120 decibels&#8221; is the same as saying &#8220;1,000,000 times&#8221; (because 10^(120\/20) = 1,000,000)*, which means that the following two sentence fragments say exactly the same thing:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8220;the sound of a jet engine at takeoff is 120 dB&#8221;<\/li>\n\n\n\n<li>&#8220;the sound of a jet engine at takeoff is 1,000,000 times louder than&#8221;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;louder than&#8221; what? THIS is the problem. The sentence should have said<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8220;the sound of a jet engine at takeoff is 120 dB <strong>SPL<\/strong>&#8221; which means <br>&#8220;the sound of a jet engine at takeoff is 1,000,000 times louder than <strong>the quietest level of a 1 kHz sinusoidal tone that an average person can hear<\/strong>.&#8221;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Without the &#8220;SPL&#8221; after the &#8220;dB&#8221;, there&#8217;s no way to know what you&#8217;re talking about, which is why, 40 years ago, I couldn&#8217;t understand what a &#8220;decibel&#8221; was &#8211; and why, 10 years later, my students had such trouble as well.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Without the &#8220;SPL&#8221;, it would be like if speed limits said that you should drive &#8220;50 km\/&#8221;. Per second? Per minute? Per hour? Per day? These are very different things&#8230; <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This also means that if you&#8217;re talking about something else, then you need a different letter after the &#8220;dB&#8221;. For example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sound Pressure Level<br>&#8220;dB SPL&#8221; means &#8220;sound pressure level relative to a sound pressure level of 20 \u00b5Pascals&#8221;<\/li>\n\n\n\n<li>Volts<br>&#8220;dB V&#8221; means &#8220;voltage relative to 1 V RMS&#8221;<\/li>\n\n\n\n<li>Volts (another version)<br>&#8220;dB u&#8221; means &#8220;voltage relative to 0.775 V RMS&#8221;<\/li>\n\n\n\n<li>Watts<br>&#8220;dB m&#8221; means &#8220;voltage relative to 1 mW&#8221;<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">and there are lots more&#8230;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In case it&#8217;s interesting, a before-and-after of the plot that I edited yesterday is here:<br><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"541\" height=\"378\" src=\"https:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/equal_loudness_crop.png\" alt=\"\" class=\"wp-image-8898\" style=\"width:298px;height:auto\" srcset=\"https:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/equal_loudness_crop.png 541w, https:\/\/www.tonmeister.ca\/wordpress\/wp-content\/uploads\/equal_loudness_crop-300x210.png 300w\" sizes=\"auto, (max-width: 541px) 100vw, 541px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">&#8230; and if you want to dig into this a little more deeply, then I wrote <a href=\"http:\/\/www.tonmeister.ca\/main\/textbook\/intro_to_sound_recordingch3.html#x14-860002.2\">this explanation<\/a> for my electroacoustic measurements course 30 years ago<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">* Four last things:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>#1: <\/strong>If you already have the measurement of the thing that you want to express in decibels relative to something else, AND it&#8217;s a pressure or voltage measurement, then the math you do is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x dB = 20 * log10(Pressure1 \/ Pressure2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, if Pressure1 = 2.5 Pascals and Pressure2 =  1.25 Pascals, then <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">20 * log10(2.5\/1.25) = 6.02 dB<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So you can say that 2.5 Pascals is 6.02 decibels relative to 1.25 Pascals.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If, instead, you use the standard reference of 20 \u00b5Pa as Pressure2, then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">20 * log10(2.5\/0.00002) = 101.9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, you can say that 2.5 Pascals is 101.9 dB SPL.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>#2: <\/strong>If you want to do it backwards for pressure or voltage then the math you do is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pressure2 * 10^(dB\/20) = Pressure1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you have the dB SPL value and you want to find out how many Pascals you&#8217;re talking about, then Pressure2 = 0.00002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, if you know that the measurement is 101.9 dB SPL, then:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">0.00002 * 10^(101.9 \/ 20) = 2.489 Pascals<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>#3:<\/strong> Some examples:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>20 * log10(4\/2) = 6.02 dB<br>&#8220;+6 dB&#8221; is the same as saying &#8220;times 2&#8221;<br><\/li>\n\n\n\n<li>20 * log10(5\/10) = -6.02 dB<br>&#8220;-6 dB&#8221; is the same as saying &#8220;times one half&#8221;<br><\/li>\n\n\n\n<li>20 * log10(100\/10) = 20 dB<br>&#8220;+20 dB&#8221; is the same as saying &#8220;times 10&#8221;<br><\/li>\n\n\n\n<li>20 * log10(20\/200) = -20 dB<br>&#8220;-20 dB&#8221; is the same as saying &#8220;times 0.1&#8221;<br><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>#4: <\/strong>If you&#8217;re measuring power (in Watts), then the math is slightly different.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Once-upon-a-time, I taught a course in electroacoustic measurements at McGill. I used to devote an entire 3-hour class to explaining decibels, partly because we use them so often in audio, partly because I had such difficulty wrapping my own head around them when I was starting off, and partly because the reason I and many [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[33,4,65],"tags":[],"class_list":["post-8896","post","type-post","status-publish","format-standard","hentry","category-acoustics","category-audio","category-measurements"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p48hIM-2ju","_links":{"self":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8896","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/comments?post=8896"}],"version-history":[{"count":3,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8896\/revisions"}],"predecessor-version":[{"id":8902,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/posts\/8896\/revisions\/8902"}],"wp:attachment":[{"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/media?parent=8896"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/categories?post=8896"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tonmeister.ca\/wordpress\/wp-json\/wp\/v2\/tags?post=8896"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}