A thunderclap is heard by someone at 60dB. Somebody 4.5km down the road hears th

Question

A thunderclap is heard by someone at 60dB. Somebody 4.5km down the road hears the same thunderclap at 40dB. How far from the lightning was the first observer, explain your answer.

Imagine an infinitely long straight highway in Kansas. The traffic along the highway produces a lot of noise. A person living in a nearby resi- dential area hears traffic to be 20dB. A goose flying at 0.01km directly over the highway hears the traffic at 40dB. Neglecting the variations in sound perception between humans and geese, calculate the distance of the residential area from the highway. Explain how you got your answer.

Explanation / Answer

1) dB1 = 10*Log(I/Io).....60 = 10*log(I1/Io)

I1 = 10^6*Io

dB2 = 10*Log(I2/Io).....40 = 10*log(I2/Io)

I2 = 10^4*Io

I2/I1 = (r1/r2)^2

(10^4)/(10^6) = (r1/4.5)^2

r1^2 = 4.5^2*10^-2

r2 = 0.45 km

2) dB1 = 10*Log(I/Io).....20 = 10*log(I1/Io)

I1 = 10^2*Io

dB2 = 40*Log(I2/Io).....40 = 10*log(I2/Io)

I2 = 10^4*Io

I2/I1 = (r1/r2)^2

(10^4)/(10^2) = (r1/0.01)^2

r1^2 = 0.01^2*10^2

r2 =0.1 km

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