Sound intensity logarithmic scale problem??

Question

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?

Answer 1

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.