An audio engineer takes decibel readings at distances of r_1 = 12m and r_2 = 22

Question

An audio engineer takes decibel readings at distances of r_1 = 12m and r_2 = 22 m from a concert stage speaker during a sound check. When he is r_1 from the speaker, the engineer registers a decibel level of beta_1 = 106 dB on his loudness meter. Randomized Variables r_1 = 12 m r_2 = 22 m beta_1 = 106 dB What is the intensity of the sound, I_1, in watts per square meter, that is measured by the loudness meter when the engine a distance of r_1 from the speaker? I_1 = Grade Summary Deduction Potential Submissions Attempts remaining: (3% per attempt) detailed view 0% deduction per feedback. How much power P, in watts, is coining from the speaker during the sound check at distance r_1? Assuming that the speaker output does not change between the two measurements at r_1 and r_2, what sound intensity level beta_2, in decibels, will the loudness meter report when the engineer is at a distance r_2 from the speaker?

Explanation / Answer

r1 = 12 m ; beta1 = 106 dB

a)We know that intentisy in dB is given by

dB = 10 log10 (I/I0)

106 = 10 log10 (I/10^-12)

solving for I we get, I = 0.039 w/m^2

Hence, I = 0.039 w/m^2

b)Intensity = Power/Area

Power = Intensity x Area

P = 0.039 x 4 x 3.14 x 12^2 = 70.54 W

Hence, P = 70.54 W

c)I = P/A

I = 70.54 W/4 x 3.14 x 22^2 = 0.012 W/m^2

dB = 10 log (0.012/10^-12) = 100 dB

Hence, beta2 = 100 dB

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