Using Logarithms to Measure Sound



Using Logarithms to Measure Sound name:

A logarithmic scale is often used to describe our perception of certain sensory stimuli, such as loudness of sound. Loudness of sound is approximately logarithmically related to the physical quantity (sound intensity) that produces it. Loudness of sound is measured in decibels (Db). To give you an idea of some known decibel levels, look at the information below:

Normal talking 40 Db

Loud home sound system 115 Db

Rock concert 155 Db

Damaging to internal organs 200 Db

Atomic bomb 255 Db

Try these problems:

Let I be the intensity of a sound, measured in[pic]. The weakest intensity that can be heard (like the sound of a pin dropping at 10 meters away) is [pic], while sound becomes painful at an intensity above [pic]. Loudness, measured in decibels (dB), is defined by the function L(I), where L is loudness in decibels and I is intensity in [pic].

L(I) = [pic][pic]

Use this information to solve the problem below:

1) An office machine produces a noise level with an intensity of [pic][pic]. How loud is this machine in decibels? An Environmental Protection Agency (EPA) regulation requires that the noise level of the office cannot exceed 90 decibels. Is this machine legal according to these regulations?

2) In order to handle an increasing workload, a second identical machine must be brought into the office. So now, with both of the machines running, the intensity is twice the intensity produced by one machine alone. How loud are both machines running together, in decibels? Is it legal according to the EPA regulations to run both machines at once?

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