Lab Quiz - Electromagnetic Standing Wave

Introduction:

                For this experiment, the frequency of the microwave, the possible dimensions for the microwave, the total energy content of the cavity, the numbers of the photons per second oscillated in the microwave, and the pressure exerted by the photons on the side of the microwave have to be analyzed or calculated. In order to get the needed data to answer all the questions, first, a plate of marshmallows had to be micro waved so that the standing wave could be produced. When the marshmallows were heated, some spots rose up and formed some sequent hills. After the marshmallows stopped being heated, some dents then would be formed, and they were known to be the antinodes of the standing waves. The distance between two antinodes had to be measured so that the wavelength of the After heating the marshmallows, a cup of water, which was 100 grams, was also micro waved for 30 seconds. Then the temperature of the heated water had to be in order to obtain the energy. Finally, with these two objected being micro waved, the dimensions of the microwave were measured with ruler. With all the measured and recorded data, the questions mentioned above had to be calculated or deduced.

 The Marshmallows were ready to be micro waved

The pattern for the heated marshmallows (the dents were where the anti-nodes w)

Then the 100 grams water were also micro waved

Data table:

Approximate pattern of the marshmallows
Distance from two antinodes	12±0.5 (cm)
Increased temperature	20±0.5 Celsius  ~  57±0.5 Celsius
Dimensions of the microwave	Width	35±0.5(cm)
	Length	35±0.5 (cm)
	Height	23±0.5(cm)

Calculation:

frequency = velocity/wavelength = 3x10^8/0.24 = 1.25x10^9 (Hz)

Dimensions:

since the standing wave is three dimensional, distance from one pop to another pop would just be the half of the wavelength.

          Length:1.5(#of waves)*24=36(cm)

          Width:1(#of waves)*24=24(cm)

           Deduced height: 20 (cm)  

Total energy content of the cavity:

          Equations: Q=mc(change of Temp)

                              =(0.1kg)*(4.184J/kg)*(57 Celsius - 20 Celsius)=15480.8(J)

Energy for one photon

          Equation: E=(hc)/λ

                           =6.626*10^(-34)*(3*10^8)/0.24=8.2825*10^(-25) (J/per photon)

Numbers of photon oscillate in the microwave per second:

          Equation:Q/E/time=15480.8/8.2825*10^(-25)/30=6.23*10^26 (photons/s)

Power:

          Equations:Power=Energy/time

                                    =15480.8/30=516.03(W)

Pressure on each side of the microwave:

          Equation: pressure=power/(area*c)

               top/bottom sides:516.03/(0.35*0.35*3*10^8)=2.14*10^(-5) (Pa)

                                 sides:516.03/(0.35*0.23*3*10^8)=4.21*10^(-5) (Pa)
          

Conclusion:

As a result, since the marshmallows were not put on the entire inside surface of the microwave, the deduced length and the width were not as the ratios of the measured data. With the concept of conserved energy, the equation, Specific Heat Capacity could be applied to obtain the total energy content of the cavity. With this obtained energy, the numbers of photon oscillated per second could also be calculated. The microwave created waves when it is heating, since the microwave is a closed box, the wave would then be bounced back to create a standing wave. Standing wave is also a type of periodical wave in which then the frequency of the wave is constant so that the wavelength could also be calculated.