Section 5.6 · Problems · 4 of 14
Problem 5.6.4: Same medium, higher frequency
Same medium, higher frequency
#The electric field component of a time-harmonic wave propagating in a nonmagnetic, lossless, source-free region is given as
- Find the frequency, period, phase velocity, wavelength of this wave.
- Determine the relative permittivity of the medium.
As in Problems 5.6.1–5.6.3: is the coefficient of , the coefficient of , and for a lossless nonmagnetic medium.
The amplitude is along , , so , and the minus sign means travel towards . The phasor is .
Lossless and nonmagnetic, :
. The phase velocity, hence the medium, is the same as in Problem 5.6.2. At times the frequency the wavelength is times shorter, .
At free space has , while in the medium : , and the field still takes to repeat in time (Figure 5.6.15a). Problems 5.6.1–5.6.4 all give from alone (Figure 5.6.15b): read and off the phase and nothing else is needed. All four assume and .
