![]() The logarithmic spiral is also called the spira mirabilis, Latin for “miraculous spiral”, named that for the unique property that while the size increases with each loop, the shape of each successive loop or curve is the same. ![]() In fact, they increase in a geometric progression, which means each loop is further from the centre than the previous one by a multiple of the previous distance.Ī logarithmic spiral, or growth spiral looks like this: The coils of watch balance springs and the grooves of very early gramophone records form Archimedean spirals, making the grooves evenly spaced (although variable track spacing was later introduced to maximize the amount of music that could be cut onto a record).Ī logarithmic spiral is a spiral that expands at an increasing rate as it moves outward from the centre. This pattern occurs in a roll of paper or tape of constant thickness wrapped around a cylinder. The points on the spiral move away from the centre by the same amount with each complete loop, like this: ![]() A geometric spiral is also known as an Archimedean Spiral, or an arithmetic spiral. In other words, the intervals on the scale increase exponentially.Ī good way to visualise this difference is to look at geometric (linear) and logarithmic spirals.Ī geometric spiral is a spiral that expands at a constant rate, like a linear scale. In a logarithmic scale, each unit represents a multiplication (or division) by a constant factor, rather than a fixed amount. On the other hand, a logarithmic scale expands at an increasing rate as it moves out from the starting point. For example, if you have a ruler with centimetre markings, each centimetre represents the same distance. It follows a constant rate of increase, where each unit on the scale represents an equal increment. A linear scale is what we encounter in our day-to-day lives. Have you ever wondered why we use logarithmic scales to measure certain quantities? Well, let’s dive into this fascinating topic and uncover the reasons behind it.įirst, let’s take a look at the difference between linear and logarithmic scales. To calculate decibels, use the following formula:, where L is loudness and is 10 -12 which is barely audible.And how are they different from linear scales? If you were standing one foot away from a loud machine, for instance, you would experience higher decibel levels than if you were ten feet away, even though the intensity of the sound produced remains unchanged. The intensity of a sound reaching a person's ear depends not only on the intensity of the sound produced, but also on the persons distance from the source of the sound. Though reducing the decibel level produced by a sound source from 80 to 77 may not seem like a major change, it would actually represent a 50% reduction in audible sound. Rather, each three decibel increment affects a 50% change in sound pressure levels. A sound with a 50 dB level is not twice as intense as a sound with a 25 dB level. However, the relationship among the values on the decibel scale is not linear but logarithmic. ![]() The intensity of sound is measured in a unit called the decibel (dB), which describes the relative intensity of a sound based on a logarithmic scale containing values ranging from 0 to 194.Ī zero value on the decibel scale represents the weakest sound audible to humans and sound intensity increases in correspondence with numeric values.
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