Question

In a test of subsonic jet, the jet flies over head at an altitude of 100 m. The sound intensity on the ground as the Jet passes overhead is 160 dB. At what altitude should the jet plane fly so that the ground noise is not greater than 120 dB?

• A. above 10 km from ground
• B. above 1 km from ground
• C. above 5 km from ground
• D. above 8 km from ground

Answer 1

The correct option is A above 10 km from ground

Loudness, $L=10\times lo{g}_{10}(\frac{I}{I_o})$

where $I=\frac{I_o}{r^2}$

$⟹L=10\times lo{g}_{10}(\frac{1}{r^2})$

Now, $160=10\times lo{g}_{10}(\frac{1}{(100{)}^2})$ ..............(1)

Let the altitude be $x$ m for the sound intensity of 120 dB.

So, $120=10lo{g}_{10}(\frac{1}{x^2})$ ..............(2)

$16-12=lo{g}_{10}\frac{1}{10000}-lo{g}_e\frac{1}{x^2}$

$4=lo{g}_{10}\frac{x^2}{10000}⟹x=10000m$$=10km$ above the ground.