A recording engineer works in a soundproofed room that is 47.5 dB quieter than the outside. If the sound intensity in the room is 1.40 x 10^-10 W/m2, what is the intensity outside?
I have done this numerous times and it is still wrong!
-47.5 = 10 log (1.4x 10^-10/1x 10^-10)
-47.5 = 10 log 1.4
Help please. I think I just confused myself!
To find the intensity outside, we need to first solve the equation:
-47.5 = 10 log (1.4 x 10^-10 / I)
Here, I represents the unknown intensity outside the room.
To isolate I, divide both sides of the equation by 10:
-4.75 = log (1.4 x 10^-10 / I)
Next, we need to convert the equation from logarithmic form to exponential form:
10^(-4.75) = 1.4 x 10^-10 / I
Now, let's solve for I:
I = (1.4 x 10^-10) / 10^(-4.75)
To simplify this calculation, remember that dividing by a number in scientific notation is the same as multiplying it by the reciprocal:
I = (1.4 x 10^-10) x (10^(4.75))
Using the property of exponents, we can simplify further:
I ≈ 1.4 x 10^-10 x 5,623.41325190349
Calculating this value will yield the intensity outside the room. Make sure to check your calculations carefully to avoid any errors.