A trumpet creates a sound intensity level of 1.12 X 10^2 dB at a distance of 0.8

Question

A trumpet creates a sound intensity level of 1.12 X 10^2 dB at a distance of 0.80 m. (a) What is the sound intensity of a trumpet atthis distance? 0.158 W/m^2 (b) What is the sound intensity of five trumpets at thisdistance? 0.79 W/m^2 (c) Find the sound intensity of five trumpets at the location ofthe first row of an audience, 6.80 m away,assuming, for simplicity, the sound energy propagates uniformly inall directions. 0.011 W/m^2 (d) Calculate the decibel level of the five trumpets in the firstrow. 100.4 dB (e) If the trumpets are being played in an outdoor auditorium, howfar away, in theory, can their combined sound be heard? 5 dB 5 Your answer differs from the correct answerby orders of magnitude. m

Explanation / Answer

Oh yeah... that's a weird question. . The idea is that 0 dB is the quietest audiblesound, so you have to find the distance at which the sound levelwould be 0 dB. This means that the intensity of the sound wouldbe   1 x 10-12 W/m2 . So the intensity would have to decrease by a factorof     0.011 / 1 x 10-12 = .          =    1.1 x1010      compared to theintensity of the first row. . Since, in theory, the sound decreases proportionally todistance squared, you can now write: .      d2 /6.802 =   1.1 x1010       so .     d =   7.13 x105   meters     is the furthest distance atwhich the sound could be heard. . So the intensity would have to decrease by a factorof     0.011 / 1 x 10-12 = .          =    1.1 x1010      compared to theintensity of the first row. . Since, in theory, the sound decreases proportionally todistance squared, you can now write: .      d2 /6.802 =   1.1 x1010       so .     d =   7.13 x105   meters     is the furthest distance atwhich the sound could be heard.

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