A train sounds its horn as it approaches an intersection. The horn can just be h

Question

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 43 dB by an observer 7 km away.
(a) Convert the noise level in dB to intensity.(b) What is the average power generated by the horn?

(c) What intensity level of the horn's sound is observed by someone waiting at an intersection 45 m from the train? Treat the horn as a point source and neglect any absorption of sound by the air.

(d) What intensity level (in dB) of the horn's sound is observed by someone waiting at an intersection 45 m from the train?Treat the horn as a point source and neglect any absorption of sound by the air.

Explanation / Answer

A) 43 db
[a] divide by 10 = 4.3
[b] raise 10 to that power = 10^4.3 = 19952.62
[c] multiply 10^-12 by 19952.62 = 1.9952*10^-8 watts/m²

B) First find the intensity of a 43dB sound using = 10dB*log(I/10^-12)

so I = 10^(43/7)*10^-12 = 1.39*10^-6 W/m^2

Now P = I*A = 1.39x10^-6*4*(10000m)^2 = 1746 W

C) at 45 m the intensity = P/A = 1746W/(4*45^2) = 0.0686 W/m2

D) This corresponds to a level of 10dB*log(0.0686/10^-12) = 108.36 dB

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