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## Time For A Free Hearing Checkup

In order to spread out the intensity of sounds so our ears are more sensitive to changes, we use logarithms to measure sound. The key equation is D = 10 log(I/I0), where D is Decibels, I is the sound's intensity, and I0 is a baseline measure of the threshold of hearing.

For example, when you talk with someone in a normal voice, you are making a sound that is one million times louder than the threshold of hearing I0. In comparison, loud rock music at a concert is a one trillion times louder than the threshold of hearing I0.

Given the above context and hints, see if you can order the following sounds according to their Decibel levels of 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 respectively.

• Whisper
• Power Mower
• Vacuum Cleaner
• Residential Street Noise
• Normal Breathing
• Threshold of Hearing
• Footsteps
• Busy Street
• Quiet Conversation
• Loud Rock Music
• Heavy Truck 20 Yards Away
• Normal Conversation

Source: Adapted from Dale Hathoway's Mathematics For the Modern World, 2000, p. 134

Hint: To lock in some comparison values, compute the Decibel levels of I0, normal conversation, and loud rock music.

Solution Commentary: The suggested ordering is:

• Threshold of Hearing - 0 Decibels
• Normal Breathing - 10 Decibels
• Whisper - 20 Decibels
• Footsteps - 30 Decibels
• Residential Street Noise - 40 Decibels
• Quiet Conversation - 50 Decibels
• Normal Conversation - 60 Decibels
• Busy Street - 70 Decibels
• Vacuum Cleaner - 80 Decibels
• Heavy Truck 20 Yards Away - 90 Decibels
• Power Mower - 100 Decibels
• Loud Rock Music - 120 Decibels
How did you do?