Apply the definitions of intensity and decibel level. Because the decibel level

Question

Apply the definitions of intensity and decibel level. Because the decibel level beta varies logarithmically with sound intensity I, three identical speakers produce a sound intensity of I_3 = 3I_1, but not a decibel level of 3 beta_1. The correct expression for the decibel level of three identical speakers is beta_3 = 10 log (3I_1/I_0), where I_1 is the sound intensity from a single speaker. Evaluate known quantities and solve for the unknown quantity. The unknown quantity to be determined is the decibel level beta_3 at a distance of 2.70 m from three identical speakers. To find beta_3, we first use the definition of decibel level beta_1 to determine I_1, the intensity from a single speaker. We have beta_1 = 10 log (I_1/I_0), where beta_1 = 86.0 dB. What is the correct value for I_1, the sound intensity at a distance of 2.70 m from a single speaker?

Explanation / Answer

We know that
Io= 10^-12 W/m^2
Substituting in the given equation we get
I1= 5.43 x 10^-9 w/m^2

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