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# Decibel Scale

Discover the magic of the Decibel Scale, the key to measuring sound intensity. Unpack the equation Beta = 10 log (I/10^-12), and marvel at the sensitivity of human hearing. Explore how logarithms transform large scales into manageable numbers, making the Decibel Scale a powerful tool in physics. Created by David SantoPietro.

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• What causes me to have ringing in the ear(which is caused by inflammation) sometimes because I have never had an ear infection(which often causes inflammation).

And why is it that my ears get pressurized sometimes even if I don't have an allergic reaction or I am not changing altitude fast enough? • Why do we even bother to use the Decibel Scale? Instead, why can't we use the Bel Scale? Or does it make your result neater... • The decibel measures sound pressure or electrical pressure (voltage) levels. It is a logarithmic unit that describes a ratio of two intensities, such as two different sound pressures, two different voltages, and so on. A bel (named after Alexander Graham Bell) is a base-ten logarithm of the ratio between two signals. This means that for every additional bel on the scale, the signal represented is ten times stronger. For example, the sound pressure level of a loud sound can be billions of times stronger than a quiet sound. Written logarithmically, one billion (1,000,000,000 or 109) is simply 9. Decibels make the numbers much easier to work with.

In practice, a bel is a bit too large to use for measuring sound, so a one-tenth unit called the decibel is used instead. The reason for using decibels instead of bels is no different from the reason for measuring shoe size in, say, centimeters instead of meters; it is a more practical unit.
• This is irrelevant but just curious; if it's a decibel shouldn't that be a tenth of a bel and you'd instead be multiplying by 1/10, not multiply by 10? Or is a "bel" equivalent to 100 * log(../...) • Don't different people have different thresholds of hearing? I mean it seems like some people can hear softer sounds than other people. Why is that? • Well part of it is how healthy your ears are which is why if you have an ear infection you can't hear as well.

Age is also a factor because old people hear in a shorter range and infants in a wider one respectively.

Genetics plays a role, in particular epigenetics which is the gene expression patterns. This could make your cochlea have more hair cells and thus you would be able to hear better.

However scientists like to work with averages instead of wide ranges and it turns out that 10^-12 W/m^2 is the average threshold of human hearing with all factors taken into consideration.
• why dosen't the intensity change the velocity of the sound wave ? • how is intensity of sound related to loudness?? • David makes things so easy to understand! Awesome teacher :) • My reference book says human ear can hear sound wave with a frequency ranging from 20Hz to 20,000Hz, and human ear has the highest sensitivity for sound wave around 3000Hz. What's the link between the frequency of sound wave and the intensity of sound wave? If the base line, lg(10^-12/10^-12) dB or 0dB, corresponds to a frequency of 2997Hz, how a human ear is possible to percept sound wave weaker than that 2997Hz? • There is no link between frequency and intensity. Intensity is the amplitude of the wave.
However the ear does not respond the same to all frequencies, so the same intensity at one frequency might sound louder than it does at another frequency. So the lowest intensity noise can be heard (according to your data, which I have not checked for accuracy) at 3000 Hz. To hear a noise at another frequency it would have to have greater intensity than that minimum that can be perceived at 3000 Hz. • Hi Chima,

As a general statement when we see 10Log(some_value) we are talking about power. If you were to talk to an electrical engineer and mention 20 Log(some_value) you would be understood to be talking about current or voltage.

Now for the math - there is a root two relationship between these values:

Power = (voltage squared) / resistance

Power = (current squared) * resistance

If you follow the log rules you will be able to see how an exponent (2 in this case) changes a 10 to 20.

Regards,

APD 