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So imagine if you measure the sound intensity at a certain spot to be $ 72$ deciBels. If you look at the SI-units used in the ratio these are $ \text{W/m}^2$. Does this mean that you can calculate the exact energy transfer per second on a given area, e.g. 2 cm2 to just be the amount of decibells you measure times the area including with the relative intensity?

I would like to calculate the energy transfer of sound.

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The decibel (dB) is a unit for expressing the ratio between two sound intensities and so has no units.

One decibel equals $10 \log_{10} \left (\dfrac{I_1}{I_2}\right )=20\log_{10} \left (\dfrac{P_1}{P_2}\right )$, where $I_1$ and $I_2$ are the intensity of the two sounds and $P_1$ and $P_2$ are the corresponding amplitudes of the pressure waves.

Examples of sound pressure is a table which illustrates the use of the auditory threshold at $1\,\rm kHz$ as the reference of $0\,\rm dB$ used on many instruments.

You may also find the Wikipedia article Sound Power of interest.

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  • $\begingroup$ Thanks for clearing that up. I changed my post. If you use as a reference intensity just atmospheric pressure, how do you calculate the energy exactly? I look at the page but I can't seem to correctly figure it out. Thanks in advance $\endgroup$
    – bananenheld
    Commented Jan 2, 2022 at 8:10
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    $\begingroup$ @bananenheld It is impossible for a sound wave to have a amplitude equal to atmospheric pressure. Note that a sound wave can be thought of as a variation in pressure about atmospheric pressure. $\endgroup$
    – Farcher
    Commented Jan 2, 2022 at 8:14
  • $\begingroup$ Ok thank you for clearing that mistake up. How can you calculate the energy then? $\endgroup$
    – bananenheld
    Commented Jan 2, 2022 at 9:34
  • $\begingroup$ Sound Intensity and Sound Level $\endgroup$
    – Farcher
    Commented Jan 2, 2022 at 9:53
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    $\begingroup$ Looking at the "Sound Intensity and Sound Level" table you will see that the reference power per square metre, $10^{-12}$, is 0 dB. So 72 dB is a power per square metre of $10^{72/10} \times 10^{-12} \approx 1.6 \times 10^{-5}$ $\endgroup$
    – Farcher
    Commented Jan 2, 2022 at 10:33

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