Experiment 7: Standing waves created by electronmagnetic waves

Objective: 

The purpose of this experiment is to study the standing waves created by the electromagnetic waves. To construct the experiment, marshmallows, microwave and a cup of water are needed. Firstly, some marshmallows are microwaved for approximately 11s. Then, a cup of water of 100g weight and a temperature of 20^oC is microwaved for 10s. Some measurements are taken. The standing wave on the marshmallows is about 12cm±1cm long from antinode to antinode. The temperature of the cup of water increases from 20 ^oC to 57 ^oC. Also, the length of the microwave is 35cm, the width is 35cm, and the height is 23cm. Based on this information, the frequency and the dimensions of the waves will be determined. Also, the total energy content of the cavity, the number of photons per second oscillating in the microwave, and the pressure these photons exert on the side of the microwave will be calculated. he concepts of heat transfer, Planck relation, and energy and momentum in electromagnetic waves are used.

 

Figure 1: marshmallows are microwaves for approximately 11s.

 

Figure 2: The standing waves created on the marshmallows after microwaved. 1.5 waves are shown. The wavelength of the standing wave is 24cm.

 Figure 3: A cup with 100g water is microwaved for 30s.

The multimeter is used to measure the temperature of the water.

Calculation:

1.      frequency of the microwave:

frequency= velocity/wavelength

= 3x10^8/0.24 = 1.25x10^9 Hz

2.      Dimensions for microwaves:

There is approximately 1.5 waves on the marshmallows. The wavelength is 24cm.

          Length:1.5*24=36cm

          Width:24cm

          Height: 20 cm

3.      Total energy content of the cavity:

         Q=mc(⊿ T)

           =(0.1kg)*(4.184J/g)*(57 ^oC - 20 ^oC)=15480.8J

4.      Energy for one photon

         E=(hc)/λ

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

5.      Numbers of photon oscillate in the microwave per second:

         = (Q/E/)time

=15480.8/8.2825*10^(-25)/30=6.23*10^26 photons/s

6.      Pressure on each side of the microwave:

         pressure=power/(area*c)

     

 Power=Energy/time

         =15480.8/30

=515.48W

               top/bottom sides: 515.48/(0.35*0.35*3*10^8)=1.40*10^(-5) Pa

                sides: 515.48/ (0.35*0.23*3*10^8)=2.13*10^(-5) Pa
          

Conclusion:

The purpose of this experiment is to study the standing waves made by electromagnetic waves. Marshmallows are used to construct this standing wave experiment because of its light weight. The standing wave made on the marshmallows was easy to detect. The standing wave’s antinode to antinode is measured to be 12cm. Therefore, the wavelength is determined to be 24cm. Using the information given, the frequency of the microwave is calculated to be  1.25x10^9 Hz using its relationship with speed of light and the wavelength. This calculated frequency is closed to the frequency of the microwave, 1.3x10^9 Hz. The dimensions of the microwaves are determined to be 24cm*36cm*20cm since there are 1.5 waves on the marshmallows. Besides, for the cup of water, with the change of temperature, the energy content of the cavity can be calculated using  Q=mc(⊿ T). Also, Planck Relation  E=(hc)/λ is used to find out the energy for 1 photon. Then, the photons per second can be found using the relationship between the total energy content, the energy for 1 photon, and the time spent to increase the temperature. The pressure can be determined using pressure=power/(area*c).