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Chapter 4: Q31E (page 1074)

The microwaves in a certain microwave oven have a wavelength of 12.2 cm. (a) How wide must this oven be so that it will contain five antinodal planes of the electric field 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 microwaves for there still to be five antinodal planes of the electric field along the width of the oven?

Short Answer

Expert verified
  1. Thewidth of the oven containing five antinodal planes is 30.5 cm.
  2. The frequency of these microwaves2.46脳109Hz
  3. The frequency of the microwaves when the length of the oven is made 5.0 cm longer is 2.11脳109Hz

Step by step solution

01

(a) Determination of the width of the oven containing five antinodal planes.

There is a spacing of half-wavelength between antinodal and nodal planes. In the oven length there is 212位=Lwavelengths fitted.

Calculate the length by substituting the required values,

L=5212.2cm=30.5cm

Thus , the width of the oven is 30.5 cm.

02

(b) Determination of the frequency of these microwaves.

The frequency is given as,

f=c位=3.00脳108m/s.122m=2.46脳109Hz

Thus, the frequency is 2.46脳109Hz

03

(c) Determination of the frequency of the microwaves when the length of the oven is made 5.0 cm longer.

In this case L = 35.5 cm given, so, solve for the wavelength,

位=2L5=235.5cm5=14.2cm

Use this wavelength value to calculate the frequency,

f=c位=3.00脳108m/s0.142m=2.11脳109Hz

Thus, the frequency is 2.11脳109Hz

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