Question

Use this technique to find a formula for the intensity I of a sound, in terms of the sound level β and the reference intensity I0. There will be a quantity (10 dB) involved in your calculations. When you enter your answer, leave off the unit dB. Express your answer in terms of β and I0.

Answer 1

The problem is basically asking us to find a way to find the sound intensity I, in terms dependent on the sound level and the reference intensity $I_0$.For this purpose we can start from the unit used in the scale logarithmic decibel, that is

$\beta = 10log_{10}\frac{I}{I_0}$

Where

I = Acoustic intensity on the linear scale

$I_0 =$ Hearing threshold

Using the logarithmic properties of the exponents the above expression can be described as:

$(\frac{I}{I_0})^{10} = 10^{\beta}$

$I = I_0 10^{\frac{\beta}{10}} \righarrow$ that is the expression or technique to find the intensity of sound.