While many standard measuring devices, such as rulers, are linear , the decibel scale is logarithmic. This kind of scale better represents how changes in sound intensity actually feel to our ears. To understand this, think of a building that is 80 feet tall. If we build up another 10 feet, the building will be Using the logarithmic decibel scale, if a sound is 80 decibels, and we add another 10 decibels, the sound will be ten times more intense, and will seem about twice as loud to our ears.
Sometimes we use different versions of decibels. While the dB scale is based only on sound intensity, the dBA scale is based on intensity and on how the human ear responds. Because of this, dBA gives us a better idea of when sound can damage your hearing. The cochlea is a snail-shaped organ inside your inner ear that allows you to hear. The cochlea can respond to a certain range of frequencies, or pitches of sound. Read more about how we hear or watch a video on how sound travels to the brain.
The cochlea responds best to frequencies in the range of human speech. All of the ratings above are taken while standing near the sound. Any sound above 85 dB can cause hearing loss , and the loss is related both to the power of the sound as well as the length of exposure. You know that you are listening to an dB sound if you have to raise your voice to be heard by somebody else.
Eight hours of dB sound can cause damage to your ears; any exposure to dB sound causes immediate damage and causes actual pain.
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All else equal here means that the frequency responses are equal and that the same input signal is used, etc. So the frequency dependence should be the same. To get a perceived doubling of loudness, you need an increase of 10 phons. So the speaker driven by the W amplifier is twice as loud as when driven by the 10 W, assuming you stay in the linear range and don't distort or destroy the speaker.
The W amplifier produces twice as many sones as does the 10 W. First, note that the neglect of reflections is very important. This calculation will not work inside a room, where reflections from the wall collectively producing reverberation make the calculation quite difficult. The constant of proportionality depends on how well the ground reflects, and doesn't concern us here, because it will roughly cancel in the calculation, provided r is reasonably large.
The difference in decibels between the two signals of intensity I 2 and I 1 is defined above to be. The difference in decibels between the two signals of power P 2 and P 1 is defined above to be. Voltage, like pressure, appears squared in expressions for power or intensity. So, by convention, we define:.
In the acoustic cases given above, we saw that the pressure ratio, expressed in dB, was the same as the power ratio: that was the reason for the factor 20 when defining dB for pressure.
It is worth noting that, in the voltage gain example, the power gain of the ampifier is unlikely to equal the voltage gain, which is defined by the convention used here. The power is proportional to the square of the voltage in a given resistor. However, the input and output impedances of amplifiers are often quite different. For instance, a buffer amplifier or emitter follower has a voltage gain of about 1, but a large current gain.
Different countries and provinces obviously have different laws concerning noise exposure at work, which are enforced with differing enthusiasm. Many such regulations have a limit for exposure to continuous noise of 85 dB A , for an 8 hour shift. For each 3 dB increase, the allowed exposure is halved. So, if you work in a nightclub where amplified music produces dB A near your ears, the allowed exposure is 15 minutes. There is a limit for impulse noise like firearms or tools that use explosive shots.
There are many documents providing advice on how to reduce noise exposure at the source ie turn the music level down , between the source and the ear ie move away from the loudspeakers at a concert and at the ear ie wear ear plugs or industrial hearing protectors.
Noise management and protection of hearing at work is the code of practice in the state of New South Wales, Australia the author's address. Sound pressure, sound level and dB. Sound is usually measured with microphones and they respond proportionally to the sound pressure, p.
Now the power in a sound wave, all else equal, goes as the square of the pressure. Similarly, electrical power in a resistor goes as the square of the voltage. The log of x 2 is just 2 log x, so this introduces a factor of 2 when we convert pressure ratios to decibels. Note, too, that a doubling of the power does not make a huge difference to the loudness. We'll discuss this further below, but it's a useful thing to remember when choosing sound reproduction equipment.
How big is a decibel? In the next series, successive samples are reduced by just one decibel. What if the difference is less than a decibel? Sound levels are rarely given with decimal places. The reason is that sound levels that differ by less than 1 dB are hard to distinguish, as the next example shows. This makes the dB a convenient size unit. Standard reference levels 'absolute' sound level We said above that the decibel is a ratio.
So, when it is used to give the sound level for a single sound rather than a ratio, a reference level must be chosen. This is very low: it is 2 ten billionths of an atmosphere.
Nevertheless, this is about the limit of sensitivity of the human ear, in its sensitive range of frequency. Usually this sensitivity is only found in rather young people or in people who have not been exposed to loud music or other loud noises. Personal music systems with in-ear speakers are capable of very high sound levels in the ear, and are believed by some to be responsible for much of the hearing loss in young adults in some countries.
So 0 dB does not mean no sound , it means a sound level where the sound pressure is equal to that of the reference level. This is a small pressure, but not zero. It is also possible to have negative sound levels: - 20 dB would mean a sound with pressure 10 times smaller than the reference pressure, i. Logarithmic measures Why do we use decibels? The ear is capable of hearing a very large range of sounds: the ratio of the sound pressure that causes permanent damage from short exposure to the limit that undamaged ears can hear is more than a million.
To deal with such a range, logarithmic units are useful: the log of a million is 6, so this ratio represents a difference of dB. Hearing is not inherently logarithmic in response. Logarithmic measures are also useful when a sound briefly increases or decreases exponentially over time. This happens in many applications involving proportional gain or proportional loss. When you measure noise levels with a sound level meter, you measure the intensity of noise called decibel units dB.
If you think about it, it would be very difficult to manufacture a sound level meter that had a linear performance, especially bearing in the mind the range of noise sources to be measured in a work environment.
It would be tricky to keep an eye on those 14 digits varying in front of you! So, to express levels of sound meaningfully in numbers that are more manageable, a logarithmic scale is used, using 10 as the base, rather than a linear one.
This scale is called the decibel scale. On the decibel scale, the quietest audible sound perceived near total silence is 0 dB. A sound 10 times more powerful is 10 dB. A sound times more powerful than near total silence is 20 dB. A sound 1, times more powerful than near total silence is 30 dB, 40 dB and so on.
When this sound is doubled this equates to a rise of 3dB decibels , using a logarithmic scale. In other words: every increase of 3 dB represents a doubling of sound intensity or acoustic power. The use of the dB unit makes it easier to measure decibels and monitor sound changes if we use these rules. The table below summarises this:.
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