Solutions/Answers to Exercises
Exercise 1. An FM radio station broadcasts on a frequency of 96.8 MHz. What is the wavelength of these radio waves in meters?
96.8 MHz = 9.68 x 107 Hz
1 Hz = 1 s-1
\(\displaystyle \lambda\;=\;\frac{2.998\times\;10^8\;m/s}{9.68\times\;10^7\;s^{-1}}\;=\;\mathbf{3.10\;m}\)
Exercise 2. A neon laser emits light at a wavelength of 625 nm. What is the frequency of this radiation, in Hz?
625 nm = 6.25 x 10-7
\(\displaystyle \nu\;=\;\frac{c}{\lambda}\;=\;\frac{2.998\times\;10^8\;m/s}{6.25\times\;10^{-7}\;m}\;=\;\mathbf{4.80\times\;10^{14}\;Hz}\)
Exercise 3. Consider the following figure.
a) Which of the waves has the highest frequency? A
b) Which would be the brightest? C
c) Which would have the longer wavelength? C
b) Which would be the brightest? C
c) Which would have the longer wavelength? C
Exercise 4. In one type of optical fiber, the wavelength of transmitted light is 1.2 x 103 nm.
a) What is the frequency?
\(\displaystyle \nu\;=\;\frac{c}{\lambda}\;=\;\frac{2.998\times\;10^8\;m/s}{1.2\times\;10^{-6}\;m}\;=\;\mathbf{2.5\times\;10^{14}\;Hz}\)
b) If the fiber optic cable is 14 km long, how long will it take for the signal to travel that distance? Assume the speed of light in the cable is 2.998 x 108 m/s .
\(\displaystyle \nu\;=\;\frac{c}{\lambda}\;=\;\frac{2.998\times\;10^8\;m/s}{1.2\times\;10^{-6}\;m}\;=\;\mathbf{2.5\times\;10^{14}\;Hz}\)
b) If the fiber optic cable is 14 km long, how long will it take for the signal to travel that distance? Assume the speed of light in the cable is 2.998 x 108 m/s .
14 km = 1.4 x 104 m
\(\displaystyle 1.4\times\;10^4\;m\times\frac{s}{2.998\times\;10^8\;m}\;=\;\mathbf{4.7\times\;10^{-5}\;s}\)