# Solved Problems-1

Problem-1
Determine the maximum number of half cycles of electric field with which it may propagate in a waveguide with a wall separation of 5 cm at a frequency of 10 GHz. Calculate the guide wavelength for this mode of propagation.
Solution
Here, we have to find the largest value of n for which the cut-off wavelength is greater than the free-space cut-off wavelength.

Free-space wavelength,

For n = 1, cut-off wavelength,

For n = 2, cut-off wavelength,

For n = 3, cut-off wavelength,

For n = 4, cut-off wavelength,

Hence, the maximum value of n is, .

Guide wavelength for n = 3, is,