Question

Airport authority has made the regulation that maximum allowable intensity level detected by a microphone situated at the end of 1630 m long runway can be 100 dB. An aeroplane when flying at a height of 200 m produces an intensity level of 100 dB on ground. while taking off, this aeroplane makes an angle of `30^@` with horizontal. Find the maximum distance this aeroplane can cover on the runway, so that the regulation are not violated (assume no reflection).

Answer 1

Since aeroplane is producing intensity level of 100 dB at a distance of 200 m from it, and this is also the maximum allowable sound level so as not to violate the regulation, The minimum distance of the plane from microphone has to be 200 m.
The diagram that follows shows the situation exactly. Let the aeroplane leave the runway, before x metres of the location of microphone. Then, PM is the shortest distance between the microphone and the aeroplane. Now,
`PM=xsin30^@=(x)/(2)`
`impliesPM=200=(x)/(2)`
`impliesx=400m`
So, the required distance is `1630-400=1230m`.