Besides the Richter scale and decibels, what are some common uses of base-10 logarithms?
Here are some other logarithmic scales:The pH scale.pH is defined as the negative base 10 logarithm of the concentration of Hydrogen Ions in an aqueous solution.It runs from about 0 for a concentration of Hydrogen ions [H⁺] of 1 unit of concentration (1 mol/L) to about 14 for the same concentration of Hydroxyl ions [OH⁻].For strong acids and bases, where [H⁺] or [OH⁻] can become > 1, values of pH < 0 or pH > 14 are well possible.The Hammett Acidity Function, H₀.The Hammett acidity function (H₀) is a measure of acidity that is used for very concentrated solutions of strong acids, including superacids.Like pH, it is also logarithmic.Concentrated sulfuric acid has H₀ ≈ -12, while fluoroantimonic acid, the most acidic substance known, has -23 < H₀ < -21, so it is one billion to hundred billion times more acidic than concentrated sulfuric acid.The naming of large numbers.We use the names Billion, Trillion, Quadrillion, Quintillion and so on to name large numbers.The names follow an arithmetic progress, Bi-, Tri-, Quadri- and so on, while the numbers themselves are each time 1000 times larger.The naming scale is therefore a logarithmic scale.So called ‘scientific’ notation.Instead of writing down all zeroes to very large or very small numbers, we write a couple of significant digits and continue with ‘times 10 to the logarithm of the order of magnitude’, also written as ‘e’ followed by ‘the logarithm of the order of magnitude’.So, Avogadro’s number is: 6.0221409×10²³ or 6.0221409e+23.The mass of the electron is: 9.10938356×10⁻³¹ kg or 9.10938356e−31 kgPlotting of logarithmic or exponential functions.By using logarithmic or double logarithmic scales for plotting of logarithmic or exponential functions, we can get their graphs as straight lines, as in this example:
Why do we use a logarithmic scale for sound intensity?
It’s because the ear responds to sound intensity logarithmically. And in turn that’s because nature produces sound intensities over an extremely wide range - if our ears could not cope with that range, there would be little purpose in having ears.So we could talk about sound intensities in terms of absolute pressure. For example, by calling the smallest possible sound we can make out ‘1’ (where 0 means silence). Then the largest sound pressure we could withstand without permanent damage would be 100,000,000,000,000 on the same linear scale. As soon as we have a lot of zeroes to deal with, the potential for error creeps in - was that 13 or 14 zeroes? A slip of the pen and you’re off by orders of magnitude.So instead, we can use a logarithmic scale, in this case ranging from 0 for the smallest sound to 140 for the loudest. Each step of 10 is 10 times the previous level. And when we use such a scale, we also find that it fits the perception of sound quite nicely - each 10 decibel step corresponds to an apparent doubling of the sound’s loudness.
How do officials record an earthquake on the Richter scale at every disaster place?
From a long years of experience we now know the spots where quakes are common.. We have seismometers there.. And in every weather station all over the world... It's one of the must have instruments for them... And yes they are always working round the clock.. As they do not require constant attention.. They basically record waves traveling through the earth. And through triangulation we can pinpoint the spot correctly. So ideally to pinpoint the epicentre you'd need readings from 3 such stations or more.. But to just know that there's been a quake somewhere 1 instrument is enough.. They do have a range 1 short range and one is long range the records are inspected daily at least in India... And monitored 24/7 to find the magnitude there are calculations . . but yes some error is expected so if there's a quake in Siberia we will get a reading but it will be a little off than what they get in Siberia but not much... 20th may is celebrated as world Meteorological Day usually then Ppl are allowed to visit and go around and get to know all instruments.. Do visit.. In your city .. Cheers
Log Word Problem Solving - TEST - Easy Best Answer?
Earthquake intensity is measured by the Richter scale. The formula for the Richter rating of a given quake is given by "R=log[I/I0]" where I0 is the "threshold quake", or movement that can barely be detected, and the intensity I is given in terms of multiples of the threshold intensity. An earthquake was reported to have a Richter number of 5.99. How does the intensity of the earthquake approximately compare with the reference intensity? I need to know how to solve this for a test tomorrow. First correct answer which explains how to do it gets best answer - I thought the answer was 0.77 but I was wrong.
Will two separate 50 dB sounds together constitute a 100 dB sound?
Your teacher is wrong, and you are (almost) right, but there's also some misinformation on this thread.Decibels can be used to measure all sorts of things, so it's misleading by itself to use the abbreviation dB without some sort of reference quantity. For example:dBm is a measure of power, where 0 dBm = 1 mWdBv is a measure of voltage, where 0 dBv = 1 V (RMS)dB (SPL) is a measure of sound pressure level, where 0 dB (SPL) = 20 μPa. It is this unit that is usually assumed when you are measuring how loud something is. You can purchase an SPL meter to take with you to concerts and make sure that the volume levels aren't going to cause damage to your hearing.A decibel is one-tenth of a bel. Bels are a logarithmic measurement of differences in either power quantities or field quantities. A bel is an order of magnitude with respect to a power quantity, or half an order of magnitude with respect to a field quantity. Power quantities include intensity and electrical power. Field quantities include amplitude, voltage, current, and sound pressure.As the other answerers said: if you double the power of your audio source, your sound pressure will increase by about +3dB (the exact value is 10*log(2) dB (SPL)). What that means is that a 50 dB (SPL) sound will go up to about 53 dB (SPL).If you just get a second identical speaker system and put it next to the first one, this will double the power consumed, but you'll experience some cancellation between the two that will complicate things. Actually, sometimes folks notice that doubling their home theater systems can actually lead to a decrease in SPL on the low end because of the exact placement of their subwoofers. So it's hard to say what will happen if you use two sound sources side-by-side unless we know exactly where they're located, where they're pointed, where the listener is located, and the characteristics of the room.If you want it to sound approximately twice as loud, you'll need to triple the pressure by multiplying the power by ten. This will take a 50 dB (SPL) sound up to 60 dB (SPL).