What is Decibels

What is Decibels?Decibel measurement and decibel levels chart

To show a signal loss or gained strength, the scientist used the unit called decibel(dB)

A decibel value in, strictly speaking, it is a ratio b/w two values

A bel is named after Alexander Graham Bell

Remember: if the decibel value is negative then the signal lost its strength similarly if the decibel value is positive then the signal got amplified or strengthened

Decibels definition: decibel  is a meter to express a ratio b/w two signals power (p_0 and p_1)

dB= deci-Bel

bel=log_{10}(p_o/p_i)

A deci-bel (dB) is one-tenth of a bel

    \begin{equation*}deci-bel(dB)=10 log_{10} \frac{p_o}{p_i}\end{equation*}

Where p_o is the output power and p_i is the input power

Decibel measurement

Consider a signal is passed through an amplifier with power 10 w  and received 20w power as output calculate whether it is gain or loss of signal strength

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    \begin{equation*}Gain=10 log_{10} \frac{20}{10} =3.01dB\end{equation*}

Consider a signal is passed through a transmission medium (cable)  with power 20 w  and received 10w power as output calculate whether it is gain or loss of signal strength

Rendered by QuickLaTeX.com

    \begin{equation*}Loss=10 log_{10} \frac{10}{20} =-3.01dB\end{equation*}

decibel levels chart

Units of sound intensity : the intensity  of sound can be expressed as power per unit area(Watts/cm^2)

ExampleDecibelsWatts/cm^2
Painful140 dB10^{-2}
130 dB10^{-3}
Discomfort120 dB10^{-4}
rock concerts110 dB10^{-5}
100 dB10^{-6}
limit for industrial noise90 dB10^{-7}
80 dB10^{-8}
70 dB10^{-9}
Normal discussion60 dB10^{-10}
50 dB10^{-11}
40 dB10^{-12}
Whisper30 dB10^{-13}
20 dB10^{-14}
Normal breathing10 dB10^{-15}
0 dB10^{-16}
-10 dB10^{-17}
-20 dB10^{-18}

Decibel scale and Amplitude

floating point
PCM Amplitude
dB16 bit PCM Amplitude
1.0032,768
0.75-2.498724.576
0.5-6.020616,384
0.25-12.04128,192
0.1-203,277
0.05-26.02061,638
0.01-40328
0.001-60.033

Mohammed Anees

Hey there, welcome to aneescraftsmanship I’m Mohammed Anees an independent developer/blogger.

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