Question

The microwaves in a certain microwave oven have a wavelength of 12.2 cm. 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?
Suppose a manufacturing error occurred and the oven was made 4.0 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?

Answer 1

Answer:

a

 $l = 0.305 \  m$

b

  $f = 3.0*10^{11} \  Hz$

Explanation:

From the question we are told that

  The  wavelength is  $\lambda  =  12.2 \  cm  = 0.122 \  m$

  The  number of antinodal planes of the electric field considered is n  =  5

The  width is mathematically represented as

       $l  =  \frac{ n \lambda}{2}$

       $l = \frac{5 * 0.122 }{ 2}$

      $l = 0.305 \  m$

Generally the  frequency the errors was made is  mathematically represented as

   $f =  \frac{c}{\lamda_k}$

Here c is the speed of light with value  $c =  3.0*10^{8} \  m/s$

     $\lambda_k$ is the wavelength of the microwave has to be in order for there still to be five antinodal planes of the electric field along the width of the oven, which is mathematically represented as

     $\lambda_k  =  \frac{ \lambda *  \frac{0.04}{2} }{n/2}$

      $\lambda_k  =  \frac{0.122*0.02}{5/2}$

So

   $f =  \frac{3.0*10^{8}}{0.000976}$

    $f = 3.0*10^{11} \  Hz$