sound intensity logarithmic scale problem??
Sound intensity logarithm problem?
The loudness of a sound L, is measured in dB (decibels) and defined as follows:
L=10log I/Io ,
where "Io" is the threshold of hearing and equal to 1 x 10^-12
and l is the sound intensity.
"The jackhammer noise is 1.5 thousand million times as intense as the softest sound."
Sound: and loudness in dB
Jackhammer : 90dB
Heavy Traffic: 75 dB
Conversational speech: 60 dB
Quiet living room: 20dB
1) the threshold of pain for hearing is 135dB. How many times as loud as a jackhammer is the pain threshold?
2) Compare the intensity of a the sound of conversation to that of heavy traffic?
3) How many times is the sound of a quiet living room as loud as that of the threshold for hearing?
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It has been a while so I am going from memory. I am sure others will correct it if needed.
The range of sound intensities is so immense that the logarithm relationship must be used to compact that range to a useful scale.
In this relationship between the log scale and the decimal system, a doubling of intensity in the decimal system is only 3dB in the log system. So for example, based on a quiet room at 20 bB, an intensity of 23 dB would be twice as loud. Therefore, the intensity of conversation at 60dB would be (60-20)/ 3 for 13.3 doublings to make it 27 times higher. This is not what we perceive, but this is the way it is measured.
You can do the rest.
Sound Intensities Decibels intensity Dp/po occasion (dB) (W/m^2) 0 10^-12 2x10^-10 Threshold of listening to 20 10^-10 2x10^-9 Whisper (at a million m) forty 10^-8 2x10^-8 Mosquito humming 60 10^-6 2x10^-7 customary communication eighty 10^-4 2x10^-6 Busy site visitors a hundred 10^-2 2x10^-5 Subway one hundred twenty a million.0 2x10^-4 Threshold of discomfort one hundred forty a hundred 2x10^-3 Jet on provider deck