Why Soft Sounds Are Pleasurable

At the other extreme of physical pain, are soft, tactile impressions that are just above the threshold of perception. Imagine a gentle wind finding its way through body hair or the lightest of drizzles falling on one’s bare shoulders. The acoustic equivalent of such pleasures is the distant sound of rustling leaves. At about 10 decibels it has less than 10 times the intensity of the faintest audible sound. And it has only one of ten trillionths of the power per area of a sound wave that could cause pain. It seems that we have evolved not only to react to extreme stimuli that endanger us but also to be rewarded when the environment toys with the lower limits of our senses.

Although the above numbers are mathematically accurate—-they are based on the formula which equates decibels with 10 times the logarithmic ratio of a sound’s intensity to our threshold intensity of 10-12 watts/meter2—they exaggerate what our eardrums actually experience.

pressurewave
from hyperphysics.phy-astr.gsu.edu  Check link for neat demo idea using methane in pipe to visualise pressure variations.

Before delving further, just what is sound? When a leaf moves back and forth, or some other body vibrates, the oscillation causes a periodic disturbance of the surrounding air molecules. The movement in one direction causes molecules of the air (or other transmitting medium) to bunch up, increasing pressure in one region. As the object reverts to its original position, a region of less crowding among molecules occurs as well. Meanwhile, the crowded region transmits its kinetic energy to other particles of the medium, repeating the pattern of high and low densities as the pressure wave propagates away from its source.

As a result, what’s more appropriate in comparing sound-strength is the use of pressure amplitude, which is proportional to the square root of a sound’s intensity. For example if our slightly rustling leaves come in at 10 dB and a pneumatic sidewalk-breaker next to us is painfully wreaking havoc at 120 dB, first we figure out the intensity ratio from the exponential version of the decibel-log formula:

I2/I1 = 10 0.1(dB2 – dB1) =10 0.1(120 – 10) = 1011.

Then by taking the square root  of 1011, we obtain the pressure ratio— about 316 000. That’s still a huge factor for how much louder the pneumatic drill is in comparison to the distant sound of gently moving leaves.

A little more number-crunching can make us appreciate how wonderfully sensitive our ears are, at least when they are working well. The exact pressure amplitude(ΔPm) of a rustling sound can be calculated from:

ΔPm = √(2Iρv) ,

where I is the intensity, and ρ and v are the density and velocity of the medium. For air at room temperature the latter numbers are 1.2 kg per meter cubed and 343 m/s, and for a 10 dB-sound, I = 10-11 W/m². Thus ΔPm is  9.07 X 10-5 pascals. Comparing it to the atmospheric pressure of 101.3 kPa, we can actually detect a difference of 1 part in a billion, and it’s enough to give us pleasure! When you consider that it takes a few parts per million of psychotropic substances to buzz the brain, something that many marvel at, to me our acute sensitivity to sound seems more remarkable, while no drugs are necessary.

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Where Have All the Clotheslines Gone?

It’s always tempting to use a simplistic view of our surroundings because, in the short term, it seems to conserve energy and appear practical. But in many cases, and certainly in the case of clotheslines, the opposite is true.

Let’s start with an apparently trivial fact about a clothesline. No matter how taut you pull it, the line sags a little under its own weight. The curve is accentuated if the line’s material is heavier or if you start hanging clothes on it. It may superficially resemble the familiar parabola from high school texts, but it’s actually closer to being a catenary described by a hyperbolic cosine function.

Parabolic shapes in both artificial situations and in nature are actually less common than people imagine. To get a parabolic path from, say, a baseball hit upwards at an angle, there would have to be only gravity acting on it. Then the angle in flight would only be the result of the diminishing and then increasing vertical component combined with a constant horizontal component. But in reality air friction and wind change the flight path into a more complicated exponential function.

The tension of a clothesline has a vertical and horizontal component at every point along its curve. Being at equilibrium the chain-tension’s vertical components balances gravity, while its horizontal components are also countered by forces in the opposite direction. The fact that the tension’s two components constantly change with the rope’s varying angle over every little length of the clothesline is what gives rise to the catenary.

Clotheslines have disappeared from many neighborhoods not only because many people do not appreciate the mathematics of pedestrian objects. If they are a rarity it’s partly because of city bylaws inspired by their perceived unsightliness and the way they hinder the view of more pleasant things like trees and sky. What gives people the luxury of giving aesthetics priority is the existence of the clothes dryer. But clothes dryers, as essential as they may be to those with small apartments and living in temperate climates, suck up a great deal of energy, an estimated 6% of all power generated in the province of Ontario, Canada, for example. Compared to the wind-and-sun-option of clothes-drying, the combination of the mechanical dryer’s tumbling action and high heat removes more lint from clothes, wearing them out faster.

While giving convenience priority over environmental matters and household budgets, people also imagine an unnecessary dichotomy between dryers and outdoor clothes lines. But clothes can also be laid out to dry naturally and discreetly in garages and on racks made for decks and balconies. Without intruding on anyone’s views,  CO2 emissions or radioactive wastes will be reduced, assuming that certain homes rely on an electrical grid still dependent on methane combustion, coal or nuclear power. If not, there are still more benefits of natural drying:

  • as we mentioned, the lengthened life cycle of clothes and the associated savings;
  • the energy that a greener grid saves can be distributed to areas with a bigger ecological footprint;
  • a smaller contribution to the heat island effect of urban areas;
  • clothes racks do not need much maintenance;
  • With less use, dryers last a lot longer. We gave a dryer to my parents and since it shares their burden of laundry with outdoor and indoor laundry lines, twenty-eight years later, it is still working.

Keep in mind that real progress lies not in developing technologies in order to be enslaved to them. We progress when we constantly evaluate their interaction with human nature and assess their health/ecological impact and adjust accordingly.

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