When standing at a certain distance from a jet on the ground on which all three

Question

When standing at a certain distance from a jet on the ground on which all three engines are running at equal power, the sound level is heard at the threshold of pain, 120 dB. If the pilot shuts down two engines but leaves the third at the same power, what is the sound level that is heard? When at a different distance, the same jet is initially heard at 95 dB. At that point after two engines are shut off, what sound level is heard? You have tuning forks (which oscillate at a fixed frequency stamped on the fork) for frequencies

Explanation / Answer

4) suppose intensity of power of each engine is W.

then intensity at distance r will I = W / 4pir^2

so I for all three engines at distance r will be same.

total intensity at point = 3I

sound level (in dB) = 10 log (I / I0)

120 = 10 log(3I / I0)

log(3I / I0) = 12

3I = I0 * 10^12 ......(i)

and when one is working then, intenisty will be I.

I = I0*10^12 /3

level = 10 log((I0*10^12 /3 ) / I0) =115.23 dB

b) 95 = 10 log (3I1 / I0)

3I1 = I0 10^9.5 ......(ii)

(i) / (ii)

I / I1 = 10^12 / 10^9.5

I = I1 (10^2.5)

W / 4pir^2 = (W / 4pi r1^2 ) 10^2.5

r1 / r = 17.78

r1 = 17.78r

that point is at 17.78 times of initial distance,

when 1 engine is working

level = 10 log ((I0*10^9.5/3 ) /I0)) = 90.23 dB

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