An audio engineer takes decibel readings at distances of r1 = 11 m and r2 = 22 m

Question

An audio engineer takes decibel readings at distances of r1 = 11 m and r2 = 22 m from a concert stage speaker during a sound check. When he is r1 from the speaker, the engineer registers a decibel level of Beta 1 = 104 dB on his loudness meter. A). What is the intensity of the sound, I1, in watts per square meter, that is measured by the loudness meter when the engineer is a distance of r1 from the speaker? B). How much power P, in watts, is coming from the speaker during the sound check at distance r1? C). Assuming that the speaker output does not change between the two measurements at r1 and r2, what sound intensity level Beta 2, in decibels, will the loudness meter report when the engineer is at a distance r2 from the speaker? An audio engineer takes decibel readings at distances of r1 = 11 m and r2 = 22 m from a concert stage speaker during a sound check. When he is r1 from the speaker, the engineer registers a decibel level of Beta 1 = 104 dB on his loudness meter. A). What is the intensity of the sound, I1, in watts per square meter, that is measured by the loudness meter when the engineer is a distance of r1 from the speaker? B). How much power P, in watts, is coming from the speaker during the sound check at distance r1? C). Assuming that the speaker output does not change between the two measurements at r1 and r2, what sound intensity level Beta 2, in decibels, will the loudness meter report when the engineer is at a distance r2 from the speaker? A). What is the intensity of the sound, I1, in watts per square meter, that is measured by the loudness meter when the engineer is a distance of r1 from the speaker? B). How much power P, in watts, is coming from the speaker during the sound check at distance r1? C). Assuming that the speaker output does not change between the two measurements at r1 and r2, what sound intensity level Beta 2, in decibels, will the loudness meter report when the engineer is at a distance r2 from the speaker?

Explanation / Answer

a) Intensity level B1 = 10*log(I1/Io);

Io = Intensity of the sound waves = 10-12 W/m2; B1 = 104 dB;

104 = 10 *{log(I1) - log(Io)};

I1 = 0.02511 W/m2

b) Intensity of sound at a distance of 11 m:

I1 = P/(4*pi*r12);

P = 0.02511*4*pi*(11)2

= 38.80 W

c) Intensity level B2 = 10*log(I2/Io);

I2 = P/(4*pi*r22);

= 0.006379 W/m2;

B2 = 10*log(0.006379/10-12);

= 98.04 dB.

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