Log 5(25) = 2 Classification of Logarithmic Units In more simple words, a logarithm is an answer to the question: “How many times do we have to multiply one number to get another number?” For example, how many times do we multiply 5 to get 25? The answer is 2 or In other words, the logarithm is a quantity representing the power to which a fixed number called the base must be raised to produce a given number. The logarithm is the inverse operation to exponentiation. Some people even think that logarithmic values more related to the era of slide rules than to the modern digital world. Looks convenient? Yes, but not to everyone! Actually, all people who are not mathematically or technically inclined can be easily confused when dealing with quantities expressed in logarithmic units like decibels. At the same time, the sound power of quiet conversation is 0.000000001 W or 30 dB SWL. For example, the sound power of a Saturn V rocket is 100,000,000 W or 200 dB SWL (dB referenced to the sound power level 10⁻¹² W, it is described below). Logarithmic units allow representing a very large range of ratios by a small convenient number similar to scientific notation. If you need to raise your voice to be heard at an arm’s length, the noise level in the environment is likely above 85 dB in sound intensity and could damage your hearing over time.The sound power of a Saturn V rocket is 100,000,000 W or 200 dB SWLĪ logarithmic scale is often used when there is a large range of quantities like sound pressure, earthquake strength, light intensity, various frequency-dependent values like musical intervals, in antenna engineering, electronics, acoustics, RF engineering. The risk of damaging your hearing from noise increases with the sound intensity, not the loudness of the sound. For example, ten violins would sound only twice as loud as one violin. In general, to measure loudness, a sound must be increased by 10 dB to be perceived as twice as loud. A sound that seems loud in a quiet room might not be noticeable when you are on a street corner with heavy traffic, even though the sound intensity is the same. Loudness refers to how you perceive audible sounds. Two sounds that have equal intensity are not necessarily equally loud. Also, the intensity of a sound at 100 dB is one billion times more powerful compared to a sound at 10 dB. This means that a sound at 20 dB is 10 times more intense than a sound at 10 dB. Instead, the intensity of a sound grows very fast. The decibel scale is logarithmic, which means that loudness is not directly proportional to sound intensity. Sound intensity is the amount of sound energy in a confined space. How loud something sounds to you is not the same as the actual intensity of that sound. For more information, visit NIOSH’s website. The time estimates listed in the “Typical Response” column are based on the NIOSH exchange rate of 3 dB. Hearing loss possible in less than 2 minutes Hearing loss possible in less than 5 minutes The maximum volume level for personal listening devices a very loud radio, stereo, or television and loud entertainment venues (such as nightclubs, bars, and rock concerts) Sounds at these dB levels typically don’t cause any hearing damage.ĭamage to hearing possible after 2 hours of exposureĭamage to hearing possible after about 50 minutes of exposureĪpproaching subway train, car horn at 16 feet (5 meters), and sporting events (such as hockey playoffs and football games) Typical Response (after routine or repeated exposure) Sounds and Noises Everyday Sounds and NoisesĪverage Sound Level (measured in decibels)
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