Physics - Intensity and the decibel scale
Intensity and the decibel scale
Loudness is not directly proportional to intensity. The characteristics of
the human ear mean that doubling the perceived loudness of a sound requires
the intensity to increase by a factor of 10. The human ear is also able to
respond to an immense range of intensities. The quietest whisper is many
millions of times weaker in intensity than the loudest sounds we can cope
with, such as roaring jet engines. This behaviour of the human ear led to
the introduction of the decibel scale. It seems that our ears hear in
factors of ten. On average, when a person indicates that they perceive the
loudness to have doubled, the intensity will actually have increased by a
factor of 10. This happens regardless of whether people are listening to
very quiet, or very loud sounds.
The ear judges the loudness of a sound through its response to the
pressure variations that occur at the eardrum. The decibel scale uses a
standard compression to rarefaction ratio to enable all sound levels to be
compared. As the response of the ear is very much affected by the frequency
of the sound heard, the scale is established with reference to a standard
frequency of 1000 Hz.
Io is referred to as the_ threshold intensity_, or the quietest sound that
the average person could detect. Io = 1 x 10 W m This is allocated a
corresponding decibel level of 0 dB. The human ear can respond to
intensities between 10 W mand approximately 100 W m. Note that the loudest
sound is 100 000 000 000 000 times more intense than the quietest sound.
The decibel scale was invented to effectively squash down this huge range
of intensities that our ears can pick up. All the values that the ear can
detect are scaled to between 0 dB and 120 dB. The conversion between
intensity (in W m) and sound level (in decibels) is shown below.
Note that there are some implications of this conversion technique. If the
intensity of a sound is increased by a factor of 10, then the corresponding
sound level shows an increase of 10 dB. A drop in intensity to one-tenth of
its original value corresponds to a drop of 10 dB. You need to familiarise
yourself with typical decibel levels of common sounds, as shown in the
* Convert 10W m into a sound level in decibels.
* Convert 50 dB into an intensity value.
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