## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 22 - Problems - Page 863: 19

#### Answer

(a) Humans are able to perceive approximately 1 octave of visible light. (b) The microwave region is approximately 13.3 octaves wide.

#### Work Step by Step

(a) The range of frequencies for visible light is about $4\times 10^{14}~Hz$ to $7.5\times 10^{14}~Hz$. We can find the ratio: $\frac{7.5\times 10^{14}~Hz}{4\times 10^{14}~Hz} = 1.9$ Since the ratio is 1.9:1, humans are able to perceive approximately 1 octave of visible light. (b) The range of frequencies for microwaves is about $10^{8}~Hz$ to $10^{12}~Hz$. We can find the ratio: $\frac{10^{12}~Hz}{10^{8}~Hz} = 10,000$ We can find the number of octaves $N$: $2^N = 10,000$ $N~ln(2)= ln(10,000)$ $N= \frac{ln(10,000)}{ln(2)}$ $N = 13.3$ The microwave region is approximately 13.3 octaves wide.

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