Question

At Cape Canaveral, on blastoff a rocket produces an intensity level of 160 dB as measured 10m from the rocket. Find the sound intensity level (in dB) and the intensity of this sound (in W/m2)

(a) 100m from the rocket

(b) 1km from the rocket

(c) 100km from the rocket

(d) Is this sound detectable by the human ear at all the distances listed? Explain.​

Answer 1

Using relation,

ß = 10 log(I/Io)

160 = 10 log(I/10^-12)

16 = log(I/10^-12)

10¹⁶ = I/10^-12

I = 10⁴

Since, intensity = P/A

=> P/(4 pi x 10²) = 10⁴

P = 4 pi x 10^6

A)

I = (4 pi x 10^6)/(4 pi x 10^4) = 100 W/m^2

dB = 10 log(100/10^-12) = 140 dB

B)

I = (4 pi x 10^6)/(4 pi x 10^6) = 1 W/m^2

dB = 10 log(1/10^-12) = 120 dB

C)

I = (4 pi x 10^6)/(4 pi x 10^10) = 10^-4 W/m^2

dB = 10 log(10^-4/10^-12) = 80 dB

D)

Since in case (A) and (B) level is greater than 120 dB, so it is detectable

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