Question

The factor of 10^−12 in the range of intensities to which the ear can respond, from threshold to that causing damage after brief exposure, is truly remarkable. If you could measure distances over the same range with a single instrument and the smallest distance you could measure was 1 mm, what would the largest be?

a) 1,000 km
b) 100 km
c) 10 km
d) 1 km

Answer 1

If the smallest distance an instrument can measure is 1 mm, and the range of distances it can measure follows the same factor as the ear's range of sound intensities (10^-12), then the largest distance it could measure would be 1,000 km.

Step-by-step explanation:

The question discusses the remarkable range of sound intensities to which the human ear can respond, highlighting the ability to detect changes over a factor of 10-12. In the context of measuring distances, if the smallest measurable distance is 1 millimeter, to find the largest distance measurable over the same range (a factor of 10-12), we need to multiply:

1 mm × 1012 = 1,000,000,000,000 mm

Converting this to kilometers (since there are 1,000,000 mm in a kilometer):

1,000,000,000,000 mm ÷ 1,000,000 = 1,000,000 km

Therefore, the largest distance that could be measured by such an instrument would be 1,000 km.