Experiment 7: Standing Electromagnetic Waves: Determination of the dimensions of a microwave, the rate of oscillating photons, and the pressure of photons on the microwave

Introduction

                The purpose of this experiment was to understand the standing waves created by electromagnetic waves, to solve the possible dimensions for microwaves by using standing waves concept, and to compute the rate of oscillating photons and the pressure exerted on the walls of microwaves by these photons.

                This experiment was conducted using a microwave, a bag of marshmallows, a paper, a cup of 100g of water, and a multimeter. Marshmallows were uniformly spread out on a paper and were microwaved for a few seconds to observe the standing wave pattern created by the electromagnetic waves. Half of the wavelength was obtained by measuring crest to crest of the marshmallows. The dimensions of the microwave were also recorded. Then 100 g of water was microwaved for 30s, and the change in temperature was recorded. The frequency and the dimensions of the microwave were computed by using the measured half wavelength. Also, the total energy content, the rate of photons oscillating in the microwave, and the pressure exerted by these photons on each dimension of the microwave were computed by using the concepts of heat transfer, Planck relation, and energy and momentum in electromagnetic waves. The following equations describing these concepts were used.

Heat transfer:                                                       Q=mc∆T                             (1)

Planck Relation:                                                   E=hc/λ                                          (2)

Energy and Momentum in electromagnetic waves:  I=P/A=p_radc                         (3) 

Figure 1: Marshmallows before being microwaved

Figure 2: Measuring water temperature after microwaving for 30s

 Video 1: Microwaving marshmallows: Marshmallows formed 3-dimensional standing waves pattern as it was being microwaved.

Data and Analysis

Table-1: Various recorded and calculated values from this experiment

Experimental measurements		Calculated values
λ/2(cm)	12.0 ± 1.0	ƒ(GHz)		1.25 ± 0.104
Length(cm)	35.0 ± 1.0	Length(cm)		36 ± 3.0
Width(cm)	35.0 ± 1.0	Width(cm)		36 ± 3.0
Height(cm)	23.0 ± 1.0	Height(cm)		20.0 ± 2.0
Amplitude(cm)	10.0 ± 1.0	Q(J)		15500 ± 466
Masswater(g)	100.0 ± 3.0	Ephotons(J)		(8.29 ± 0.691)x10-25
Tempi(˚C)	20.0 ± 0.05	Rate(photons/s)		(6.23 ± 0.833)x1026
Tempi(˚C)	57.0 ± 0.05	Power(W)		516 ± 54
Time(s)	30.0 ± 3.0	pphotons(μPa)	35x35	14.0 ± 2.72
			35x23	21.4 ± 5.77

Figure 3: Marshmallows after being microwaved: The second image showed that the places with most marshmallows were antinodes and those with very few marshmallows were nodes. 

Calculations of uncertainties

Conclusion

                In this experiment, the wavelength of the standing waves created by microwave was considered to be 24cm since the length from crest to crest of the marshmallows shown in figure 3 were 12cm apart. According to table 1, the computed dimensions of the microwave were 36x36x20 which were within the uncertainties of the measured values 35x35x23. The computed length and width of the microwave were greater than that of the measured values. This was because it was assumed that in each dimension of the paper, there was one and a half wave. In fact, as shown in figure 3, there was less than one and a half wave. Hence, the possible length and width should have been smaller than 36x36. In addition, the amplitude of the standing wave was measured to be 10cm which was a half of the height of the microwave. Therefore, the height was considered to be 20cm, but it was only an approximation. Therefore, it had a large uncertainty. If the height could not be approximated, the height of the microwave could possibly be any height approximately equal to or greater than 10cm in this particular case. If it was a lot lower than 10cm, standing waves will not possible be observed due to compression on marshmallows by the height limit.

                According to table 1, the frequency of the standing microwave was 1.25GHz, and it was computed by using the relationship between the speed of light, the frequency, and the measured wavelength. The result was within the normal range, 1-300GHz*, of the frequency emitted from a microwave oven. Besides, the heat content which was 15500J was also computed by using the measured mass and the temperature change of 100g of water. Moreover, computation revealed that there were (6.23 ± 0.833)x10²⁶ photons oscillating in the microwave in a second. These photons exerted 14 to 21.4 μPa on each wall of the microwaves. This result was obtained by using equation 3 described in the introduction. Lastly, the power of the microwave was experimentally calculated to be 516W, which agreed with the power produced by a typical consumer microwave ranging from 400W to 1200W*.

*source: Frequency of a Microwave, Power of a Microwave