The microwaves in a certain microwave oven have a wavelength of 12.2cm. a) How w

Question

The microwaves in a certain microwave oven have a wavelength of 12.2cm.
a) How wide must this oven be so that it will contain six nodal planes of the microwave disturbance (including the nodal plane at each walls) along its width in the standing wave pattern?
b)What is the frequency of these microwaves?
c) Suppose a manufacturing error occurred and the oven was made 5.0 cm longer than specified in part (a). In this case, what would have to be the frequency of the microwave for there still to be six nodal planes of the microwave disturbance along the width of the oven?

Explanation / Answer

a) The spacing of the nodal planes is
Wavelength/2
So if there are 6 nodal planes, the width must be:
6 * Wavelength/2 = 3 * Wavelength = 3 * 12.2 (cm) = 36.6 (cm)

b) The frequency is:
f = c/Wavelength = (3 * e8 / (12.2cm/100cm) ) (Hz) = 2.46e9 (Hz) = 2.46 * 10^9 (Hz)

c) If the width is:
36.6 + 5 = 41.6 (cm)
the wavelength would have to be:
WL' = 41.6/3 = 13.67 (cm), and:
f' = c/13.67 = 3e8/(13.67cm/100cm)) = 2.19 * 10^9 (Hz)

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