A trumpet creates a sound intensity level of 1.13 102 dB at a distance of 1.20 m

Question

A trumpet creates a sound intensity level of 1.13 102 dB at a distance of 1.20 m.

(a) What is the sound intensity of a trumpet at this distance?

0.1995 Correct: Your answer is correct. W/m2

(b) What is the sound intensity of five trumpets at this distance? 0.9976 Correct: Your answer is correct. W/m2

(c) Find the sound intensity of five trumpets at the location of the first row of an audience, 6.90 m away, assuming, for simplicity, the sound energy propagates uniformly in all directions. 0.03 Correct: Your answer is correct. W/m2

(d) Calculate the decibel level of the five trumpets in the first row. 119.99

Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 10%. Double check your calculations. dB

(e) If the trumpets are being played in an outdoor auditorium, how far away, in theory, can their combined sound be heard? 6.89e6

Incorrect: Your answer is incorrect. Your response differs from the correct answer by more than 100%. m

Explanation / Answer

a) Sound Intensity Level Formula

IL = 10*log10(I/I0)

I = sound intensity

I0 = reference intensity = 10^(-12) W/m^2

I = 10^(IL/10)*I0

I = 10^(1.13*10^2/10)*10^-12 =0.1995 W/m^2

b) 5 trumpets would produce 5*0.1995W/m^2 = 0.9975 W/m^2

c) Since sound is an inverse square law we have 0.9975*1.20^2/6.90^2 = 0.03 W/m^2

d) = 10db*log(0.03/10^-12) = 104.77 dB

e) The threshold of hearing has an intensity of 10^-12W/m^2

so 0.03*6.9^2/r^2 = 10^-12

so r = sqrt(0.03*6.9^2/10^-12) = 1.195*10^6m

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