During takeoff, the sound intensity of a jet engine is 140 dB at a distance of 2

Question

During takeoff, the sound intensity of a jet engine is 140 dB at a distance of 25 m.

a) What is the sound intensity in W/m2?

W/m2

b) If you are standing at this location for 1 minute, how much energy will be transferred to your eardrum? (Assume that your eardrum is 6.0 mm in diameter.)

J

c) What is the sound intensity in W/m2 if you are standing 1 km from the jet?

W/m2

d) What is the new decibel rating at this distance?

dB

e) How far from the jet would you need to be standing to hear a sound with a decibel rating of 70 dB?

m

Explanation / Answer

here,

part a:
Sound intensity level , L = 140 db
distance, r = 25 m

Sound intensity level is defined as:

L = 10*log( I / I) --------------------------(1)

with I= 10^-12 W/m^2 threshold of hearing
Hence:
I = I *10^(L/10) ----------------------------(2)

I = 10^-12*10^(130/10)
I = 10 Watts/m^2

Part B:
Intensity of osund is given as:
I = P / ( 4 * pi * R^2) ( P is Power, r is radius )

So the sound power of the aircraft engine is:
P = I*4*pi*R^2
Energy/time = I*4*pi*R^2
Energy = I*4*pi*R^2 * time ------------------------(3)
Energy = 10 * 4 * pi * (6*10^-3/2)^2 * 60
Energy = 0.06786 J

Part C:
r = 1 km = 1000 m

Rewriting eqn 3 for solution of Sound Intensity, I

I = Energy/(time*4*pi*r^2)

I = 0.06786/(60*4*pi*1000^2)

I = 9*10^-11 Watt/s^2

Part D:
From Eqn 1 , L = 10*log( I / I)
L = 10*log( 9*10^-11/10^-12)
L = 19.5424 dB

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.