4/11/2024 0 Comments Decibel scale common sounds![]() ![]() ![]() Without use of the decibel, the scale on which we’d have to put these sounds would be so large as to make representation very hard. Decibels are very good at representing those differences of magnitude. For one, acoustic pressures cover a very wide range of scales, with the sound pressure produced by leaves rustling in a forest being one trillionth of the pressure produced by a jet engine. There are several practical reasons why decibels are so widely used in acoustics. The logarithm function makes decibel values much more manageable than simple pressures, by making exponential relationships into linear ones. Then we multiply by 20, giving us a final value of 40 dB! If, instead, we had a very loud room at 200 mPa, and go through the same process, we get a value of 80 dB! And the sound of a concert at 20 Pa would be 120 dB. We take the base 10 logarithm (which translates the number to a power of ten), which gives us 2. We divide by 20 µPa (the reference pressure used for sound), giving us 100. And while this does cover a large range, even very loud sounds still have pressures well below atmospheric pressure, at around 101,000 Pa at sea level.įor a simple example of calculating decibels, consider a quiet room with a normal background sound of 2 mPa. Sounds cover a wide range of pressures, with very loud sounds being hundreds of Pascals, and the quietest being measured in micro Pascals (µPa). So, what value do we insert into the above equation to find decibels? While you can represent sounds in terms of energy or power, the most common measure is pressure, with the SI unit of Pascals (Pa). Finally, we multiply the resulting value by either 10 or 20 (depending on what we are measuring) and we have expressed our initial value in decibels! Because matters of scale tend to follow exponential rules, this operation makes these values much more manageable. After dividing by the reference, we take a logarithm, an operation which turns exponentially spaced values into linearly spaced ones. To find the decibel value for a given measurement, we must first take a ratio of that quantity with what is known as a “reference.” With all measures of scale, it is a matter of comparison, and the reference value is simply what we are comparing our current measurement to. In many ways, the decibel is the unit that best handles data whose magnitude varies greatly. We talked about how the wavelengths of sound cover a wide range of scales, and how it is the relative size of an object compared to that wavelength that determines its impact on sound. In a previous article we talked about the concept of scale, and how it relates to wavelength. Since that time, the decibel has been adopted in many different fields, notably acoustics. ![]() Originally used to measure power loss in telecommunication systems, this unit was valuable because it transformed the laborious task of multiplying losses from different portions of the system into a problem of simple addition. The decibel was first invented by Bell Laboratories in the 1920’s. We will also talk about how adopting a metric like the decibel can change the way we interact with the world. ![]() Today, we are going to look a little more at acoustic pressure, and one of the most valuable units for measuring sound: the decibel. Last time, we discussed the concepts of equilibrium and acoustic pressure, and how almost any variation around equilibrium can bear a striking resemblance to the behavior of sound. Loudness is a measure of sound intensity taking frequency into account, and is called a A-weighted decibel, dB(A), or a phon.Welcome to the fifth installment of The World Through Sound. This is a standard threshold, but it also depends on frequency. \)s o is the reference pressure which is 20 micropascals or 0 dB, and s is the observed sound pressure.The human ear has a standard sound threshold of 120 dB, which expressed logarithmically is around 10 12. ![]()
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