The threshold of hearing for the human ear is 10⁻¹² W m⁻². This is taken as the standard level. The intensity of sound is 1 Wm⁻². It has intensity (in dB).(a) 10¹² dB(b) 12 dB(c) 240 dB(d) 120 dB
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The range of sound intensity that humans can detect is so large ( spans 13 orders of magnitude). The intensity of the faintest sound that is audible is called the Threshold of Hearing. This has an intensity of about 1×10−12Wm−2.
Because it is difficult to gain intuition for numbers in such a huge range it is desirable that we come up with a scale to measure sound intensity that falls within a range of 0 and 100. That is the purpose of the decibell scale (dB).
Since logarithm has the property of taking in huge number and returning a small number the dB scale is based on logarithmic scaling. This scale is defined such that the Threshold of Hearing intensity has a sound intensity level of 0.
The intensity level in dB of a sound of intensity Iis defined as:
(10dB)log10(II0); Io - intensity at the threshold of hearing .
This Problem :
I=5×10−6Wm−2; Io=1×10−12W.m−2
The sound intensity level in dB is :
(10dB)log10(5×10−6Wm−21×10−12Wm−2)=66.99dB
Because it is difficult to gain intuition for numbers in such a huge range it is desirable that we come up with a scale to measure sound intensity that falls within a range of 0 and 100. That is the purpose of the decibell scale (dB).
Since logarithm has the property of taking in huge number and returning a small number the dB scale is based on logarithmic scaling. This scale is defined such that the Threshold of Hearing intensity has a sound intensity level of 0.
The intensity level in dB of a sound of intensity Iis defined as:
(10dB)log10(II0); Io - intensity at the threshold of hearing .
This Problem :
I=5×10−6Wm−2; Io=1×10−12W.m−2
The sound intensity level in dB is :
(10dB)log10(5×10−6Wm−21×10−12Wm−2)=66.99dB
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the actual answer is 0 decibel
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