The 10,000-fold gap drawn as 57% more bar

The bar with no true zero The logarithmic unit

Dark navy slide, masthead “Family meeting · kitchen table · the case for Saturday night’s concert” on the left and “Six everyday sounds · decibels as published by the CDC” on the right, headlined “A rock concert is barely half again as loud as the washing machine.” A tag reads “Demonstration · drawn by us from CDC Vital Signs, February 2017 · the family and its eldest are invented”. A standfirst says the chart shows six sounds at the decibel level the Centers for Disease Control and Prevention gives for each, exactly as printed, on an axis that starts at zero with even 10 dB ticks and nothing cropped, broken or capped; it reads off the chart that the rock concert’s bar is 110 against the washing machine’s 70, 57% longer, and only 10% longer than the sporting event the family already goes to most weekends. The main panel, headed “How loud is Saturday, really?”, is a horizontal bar chart on a linear axis from 0 to 130 decibels: washing machine 70 dB, traffic noise inside a car 80 dB, leaf blower 90 dB, sporting event 100 dB, rock concert 110 dB in gold with the words “just 57% more bar than the washing machine” printed inside it, and siren 120 dB; the 80 dB label sits inside the end of its bar. A dashed gold line at 85 dB is labelled “CDC: 85 dB, where extended exposure can cause damage”. Five cards run down the right. “The gap, in one figure” prints 1.57× and says forty decibels between the concert and the washing machine are four gridlines, under a third of the frame. “Compared with things we already do” lists the concert’s bar against the others: +57% over the washing machine, +38% over traffic inside the car, +22% over Dad’s leaf blower and +10% over the sporting event. “The leaf blower question” says the leaf blower runs every Saturday morning at 90 dB, which is 82% of a rock concert, every week, all autumn, that nobody has called a family meeting about it, and that one evening at 110 is one more gridline. “Recommendation” says to approve Saturday, since the gap between the concert and the sporting event is the width of one gridline and the siren on the end of the chart is louder than both. “Nothing on this slide is bent” says every number is the CDC’s, on a zero-based linear axis with even ticks, no truncation, no log scale and no second axis. A footer credits CDC Vital Signs, “Too Loud! For Too Long!”, February 2017, lists the six published levels and the CDC’s 85 dB statement, and says the family, the meeting and the recommendation are invented while every decibel figure is the CDC’s. — Showing the misleading chart

The same six sounds on a cream background, masthead “The same six sounds · the same six CDC figures · three rulers” and “+10 dB = ×10 sound intensity”, headlined “The 10,000-fold gap drawn as 57% more bar”. A standfirst says nothing on the slide was cropped and every decibel is the CDC’s; that a decibel is ten times the base-ten logarithm of a ratio of a sound’s intensity to a reference near the quietest sound a young ear can hear at about 1 kHz, so every 10 dB is another ×10 and a bar drawn from 0 dB measures how many tenfold steps a sound sits above that reference; that un-logged, the concert carries 10,000 times the sound intensity of the washing machine; and that by the CDC’s own figures 2 hours of the leaf blower can cause damage, and 2 minutes of the concert. The main panel, “One set of sounds, three rulers”, puts the six sounds in rows across three linear panels. Panel 1, “Decibels: the slide’s numbers, as dots”, places a dot for each sound from 70 to 120 dB with a dashed line at 85 dB, noting that the dots mark positions only, since 0 is a reference rather than silence, and that each 10 dB is ×10, four steps from the washing machine to the concert. Panel 2, “Sound intensity, un-logged”, in watts per square metre on a zero-based axis to 1, draws the siren as a full-width bar at 1, the rock concert in red at 0.1, a tenth as long, the sporting event as a sliver at 0.01, and the leaf blower, traffic and washing machine at 0.001, 0.0001 and 0.00001, each under a pixel and drawn at a two-pixel minimum; a note says the three together come to 0.00111, about a 900th of the siren. Panel 3, “Exposure that can cause damage”, in minutes as the CDC gives them, with a note that a longer bar means more time before damage, draws the leaf blower at 2 hours, the sporting event at 14 minutes, the rock concert in red at 2 minutes and the siren at 1 minute, with the washing machine and traffic marked “below 85 dB · no time given”; a note says the concert gets a sixtieth of the leaf blower’s time, 20 dB apart. Four cards run down the right. “How much louder is the concert?” tabulates the concert against each quieter sound by bar length, intensity and rule-of-thumb loudness: washing machine 1.57×, 10,000× and about 16×; traffic 1.38×, 1,000× and about 8×; leaf blower 1.22×, 100× and about 4×; sporting event 1.10×, 10× and about 2×, with a footnote that +10 dB sounding about twice as loud is an approximation for steady sounds, not a measurement of these six. “What 0 dB is” says 0 dB is not silence, since silence would be minus infinity and the scale has no reachable zero, but the reference of 20 micropascals, about 10⁻¹² W/m², near the threshold of hearing, that quieter sounds come out negative, and that the washing machine’s bar is seven tenfold steps above the reference and the concert’s eleven. “The leaf blower question, again” says the leaf blower, at 90 dB, is past the 85 dB line too and worth earplugs of its own, but that the concert is 20 dB further, 100 times the intensity, with a sixtieth of the time. “What to do instead” says to plot exposure time for a safety question, to use dots rather than bars for decibels and print what a step multiplies, including that on the CDC’s figures the concert gets a sixtieth of the leaf blower’s time to possible damage, and closes: if you go, take earplugs, as the CDC advises near loud noise. A footer credits the CDC figures and says the intensities were computed by us from the published levels with the standard reference, treating each as a sound pressure level in open air, and notes that the CDC states no weighting or distance, so the intensities should be read as orders of magnitude. — Showing the misleading chart

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A slide made for a family meeting puts six everyday sounds on a bar chart, each at the decibel level the CDC gives it, on a linear axis from zero with nothing cropped. The rock concert’s bar is 110 against the washing machine’s 70, so the slide concludes that the concert is barely half again as loud. But a decibel is a logarithm: every 10 dB is another tenfold step in sound intensity, and 0 dB is a reference point rather than silence. Un-log the same six numbers and the concert carries 10,000 times the washing machine’s sound intensity. On the CDC’s own figures, 2 hours of the leaf blower can cause damage, and 2 minutes of the concert.

Centers for Disease Control and Prevention, “Too Loud! For Too Long!”, CDC Vital Signs, February 2017: washing machine 70 dB, traffic noise inside a car 80 dB, leaf blower 90 dB (2 hours can cause damage), sporting event 100 dB (14 minutes), rock concert 110 dB (2 minutes), siren 120 dB (1 minute); “85dB is the approximate point at which extended exposure can cause hearing damage.” Sound intensities computed by us from the published levels, 2017Added October 1, 2026

01The claim

Six everyday sounds, each at the decibel level the CDC gives it, and every figure exactly as printed: washing machine 70 dB, traffic inside a car 80, leaf blower 90, sporting event 100, rock concert 110, siren 120. The bars start at zero, the axis is linear with even 10 dB ticks, and nothing is cropped, broken or capped, so every bar is exactly as long as its number. Read off the chart: the rock concert’s bar is 57% longer than the washing machine’s, 22% longer than the leaf blower that already runs every Saturday morning, and 10% longer than the sporting event the family goes to most weekends. So, says the eldest at the kitchen table, Saturday’s concert is barely half again as loud as the laundry, and the case for going makes itself.

02The trick

Every number on that slide is right, and the bars are drawn exactly to scale. The problem is that a decibel is not an amount of sound. It is ten times the base-ten logarithm of a ratio: a sound’s intensity compared with a reference of about 10⁻¹² watts per square metre (20 micropascals of pressure), chosen because it sits near the quietest sound a young ear can hear at about 1 kHz. Two things follow, and the slide trips on both. The first is the logarithm. Every 10 dB is another tenfold step, so the 40 dB between the washing machine and the concert is four tenfold steps, which works out to 10,000 times the sound intensity. The concert carries 100 times the intensity of the leaf blower and 10 times that of the sporting event, where the bars say 1.22 and 1.10. A linear axis with evenly spaced ticks is already acting like a log axis here, because the unit has the logarithm built in, and nothing on the page says so. The second is the zero. 0 dB is not silence: silence would be minus infinity, so the scale has no zero it could ever reach. 0 dB is just the reference it counts from, and quieter sounds come out negative. So a bar drawn from 0 dB does not show how much sound there is. It shows how many tenfold steps above the reference the sound sits: seven for the washing machine, eleven for the concert. Dividing one bar by another divides those step counts, and 11 ÷ 7 is where the 1.57 comes from. Neither 1.57 nor 10,000 is how loud the concert sounds, either. The ear compresses as well, and the usual rule of thumb is that +10 dB sounds roughly twice as loud, which puts the concert at about 16 times the washing machine to the ear. That is an approximation for steady sounds, not a measurement of these six, but it is nowhere near 1.57. The number that matters for this decision is on the same CDC page as the decibels: 2 hours of the leaf blower can cause damage, 14 minutes of the sporting event, 2 minutes of the concert and 1 minute of the siren. These are exposures that can cause damage, not guarantees of safety below them, but the comparison holds: the concert is 20 dB past the leaf blower and gets a sixtieth of its time. The CDC does not state a weighting or a distance for these levels, which are typical figures for each kind of sound, so the intensities are orders of magnitude rather than measurements. (Both drawings are ours. The family and the meeting are invented, and every figure behind them is the CDC’s.)

03The fix

Ask what the decision needs. For “is this safe?”, the answer is exposure time, and on a linear axis of minutes the question answers itself: the leaf blower’s bar is 2 hours long, the concert’s is 2 minutes, and the washing machine and the car do not get a time at all because they sit below the CDC’s 85 dB line. If the question is how much sound there is, un-log it: on a zero-based axis of watts per square metre the siren fills the frame, the concert is a tenth of it, the sporting event is a sliver, and the three quietest sounds together come to about a 900th of the siren. If decibels have to appear, and they often should since they are what meters and safety guidance print, draw them as dots on a scale rather than as bars from zero. Then print what one step multiplies right next to the axis: +10 dB is ×10 in intensity and roughly ×2 to the ear. The same goes for any comparison quoted in words. Turn a gap in decibels into a ratio before calling it “half again” or “10% more”. The honest version of the slide can still say yes to Saturday, with the advice printed on the same CDC page: avoid noisy places where you can, and use earplugs, ear muffs or noise-cancelling headphones when you can’t.