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)(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:

`((I)/(I_0))^(10) = 10^(\beta)`

`I = I_0 10^{(\beta)/(10)} \righarrow` that is the expression or technique to find the intensity of sound.