Friday, February 14, 2014

Aaron's stereo produces sound at 80 dB. If the apartment building has a noise limit of 40 dB, how many times as intense is that from Aaron's stereo?

The decibel is a scale which is used in acoustics to
measure sound levels. The zero of the scale is the threshold of hearing which is
approximately the intensity of sound created by a mosquito flying 3 m away. This is
taken as the lowest sound level that an average person can hear and given a value of 0
dB.


The decibel scale is a logarithmic one where an
increase of 10 decibels increases sound intensity ten times. For example, a sound level
of 20 dB has an intensity 10 times that of a sound level of 10 dB
.


In the given problem Aaron plays music at 80 dB while the
apartment building has an upper limit of 40 dB. The intensity of the sound from Aaron's
stereo is 10^[(80 - 40)/10] = 10^4 = 10,000 times the acceptable
limit.

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