Jet Engine Sound Intensity Calculation with Absorption Effects

[JazzCarrot]

Homework Statement

$$I=\frac{p_{ave}}{4\pi r^{2}}$$ is derived on the assumption that the transmitting medium does not absorb energy. It is known that the absorption of sound in dry results in a decrease in energy of about 8 dB/km. The intensity of sound at a distance of 120 m from a jet engine is 130 dB. You should take the hearing threshold: I₀ to be 10-12 W/m²

(a) Find the intensity in dB of the sound at a distance of 2.6 km from the engine assuming that there is no absorption of sound by the air.

(b)Find the intensity in dB of the sound at a distance of 2.6 km from the engine assuming that the sound diminishes at a rate of 8 dB/km.

Homework Equations

$$I=\frac{p_{ave}}{4\pi r^{2}}$$

$$\beta =10log\frac{I}{I_{0}}$$

The Attempt at a Solution

I think I've got part (a) correct, which is 103db, from converting 130db to an Intensity, and then finding the Power, and then recalulating the Intensity at the new distance. It's just part (b) I'm struggling with, I'm not sure how to tackle it, 8db is a tiny fraction of Intensity compared to the 103db, so my answer, hardly changes... in fact, it's still 103db.

Any pointers would be welcomed!

 

[korican04]

Sorry but isn't I= pave/(4*pi*r^2) ?

 

[JazzCarrot]

Oops! Yeah should be the other way round. I'll correct that.