The speed of light is a fundamental natural constant that can be measured with high accuracy. In this experiment, a microwave oven, a Chocolate bar and butter are used to visualize standing waves1[Standing waves: A wave formed by the superposition of two counter-propagating waves, creating stationary oscillation patterns] and calculate the speed of light. By measuring the wavelength2[Wavelength: The distance between two consecutive identical points in a wave, such as two wave crests] and applying the wave equation3[Wave equation: A mathematical formula that describes the relationship between wavelength, frequency, and propagation speed of a wave], the speed of light can be experimentally determined.
1. Introduction
The speed of light in a vacuum is approximately 299,792,458 m/s and is one of the fundamental physical constants. Electromagnetic waves, such as those generated in microwave ovens, propagate at the speed of light. The waves reflected inside the microwave create standing waves, which result in uneven heating. These characteristic heating patterns can be used to determine the wavelength of microwaves and, from this, calculate the speed of light.
2. Material and Methods
Material:
- A chocolate bar
- 50 – 100 g Butter
- A microwave oven with a deactivatable turntable
- A ruler or measuring tape
Procedure:
- If the microwave has a turntable, deactivate it or place a fixed glass plate inside.
- Place a bar of chocolate with the smooth underside facing upwards on a microwave-safe plate and place it in the microwave.
- Set the microwave to 600-800 W and heat the chocolate bar for 10-20 seconds until the first melting points appear.
- Measure the distance between two adjacent melting spots (λ/2).
- For a more accurate measurement, melt 50 – 100 g butter (not margarine) and pour onto a mold in which a smooth, thin and even layer of butter forms. Place the butter in the fridge to solidify. Then proceed as described in step 3.
- Calculate the wavelength with λ=2×distance between melting spots.
- Determine the speed of light using the wave equation:
where
is the typical frequency of a household microwave.
3. Results
During the experiment, it was observed that chocolate bar started melting at specific points while other areas remained mostly solid. These melting points appeared regularly along the chocolate bar, forming a recognizable pattern. The first visible melting spots appeared within seconds, intensified with longer heating, and were precisely located at the expected positions of the antinodes4[Antinode: The point of a standing wave where the oscillation amplitude is at its maximum] of the standing wave.
Melting points also form on the butter, which are much more clearly defined.
The distance between two melting points on the chocolate bar is 5.07 cm, resulting in a wavelength of:
The calculated speed of light is then:
This value is relatively close (~83 %) to the real speed of light.
When evaluating the experiment with butter, the following picture emerges:
The distance between two melting points on the butter layer corresponds to 6.11 cm, resulting in a wavelength of:
The calculated speed of light is then:
This value is very close (~99.87 %) to the real speed of light.
4. Discussion
The experiment with the microwave and the melting points on the chocolate vividly demonstrates how microwave radiation interacts with matter and how these interactions lead to the formation of standing waves. Microwave radiation is a form of electromagnetic radiation5[electromagnetic radiation: A form of energy that propagates through space as waves of electric and magnetic fields. It includes various wavelengths such as light, X-rays, and microwaves]. Microwaves are used in microwave ovens to excite water and fat molecules in food. In a microwave oven, microwaves are generated and reflected throughout the interior. When these microwaves hit food, the molecules within it start moving rapidly, generating heat — a process we perceive as heating. However, this heating is not evenly distributed throughout the microwave oven, as the microwaves are reflected by walls and other surfaces. This results in certain areas of the microwave oven experiencing stronger radiation, while others are weaker.
Chocolate contains fat and sugar, which have different chemical properties. Microwave radiation primarily heats molecules that are efficient at absorbing microwave energy — mainly water molecules and fatty acids. When the microwave radiation hits the chocolate, this energy is absorbed by the fat molecules, causing them to vibrate faster and thereby increasing the temperature. This temperature rise causes the chocolate to melt [melt: The process in which a solid changes into a liquid due to an increase in temperature]. This explains why chocolate melts in the microwave.
Microwave radiation has the ability to reflect within the microwave oven, leading to stronger radiation in certain spots and weaker radiation in others. The areas where the radiation is strongest are where the most heating occurs — these areas are called the “bends” or “antinodes” of the standing wave. In the areas with minimal radiation, called “nodes,” the temperature remains low, so no melting occurs. This phenomenon is known as standing waves6[standing waves: Waves that occur when two waves of the same frequency and amplitude travel in opposite directions and overlap, creating stationary points (nodes) and points of maximum movement (antinodes)]. These standing waves produce regular melting patterns that resemble a series of antinodes and nodes.
The experiment with butter yields more accurate results because butter has a higher water content and melts at a lower temperature than chocolate. As a result, butter responds more quickly and evenly to microwave radiation, producing a sharper and more defined melting pattern. Butter has a simpler chemical structure than chocolate, which is made up of a mixture of fat and sugar. This means the melting process of butter is less affected by varying components, and the standing waves are clearer and more easily measurable. Moreover, butter melts at temperatures where the microwave radiation has a stronger effect, leading to a more precise melting pattern. Therefore, butter responds more efficiently and evenly than chocolate due to its chemical composition.
The standing waves in the microwave create characteristic melting spots that appear at regular intervals — these are the antinodes of the standing wave. To calculate the speed of light, the distance between two adjacent melting spots is measured, which corresponds to half the wavelength of the microwave radiation (λ/2). Once the distance between the melting spots is measured, the wavelength λ can be calculated by doubling the measured distance. With the known frequency f of the microwave radiation (which is specified on the microwave oven), the speed of light c can then be calculated using the wave equation:
where c is the speed of light, λ is the wavelength, and f is the frequency of the microwave radiation. This allows for an experimental determination of the speed of light, which may slightly deviate due to reflections from the walls of the microwave oven but still provides an impressively accurate estimate of the physical speed of light.
Overall, this experiment not only illustrates the fundamental physical principles of wave propagation and electromagnetic radiation but also shows how everyday materials like chocolate and butter can be used to measure physical constants, such as the speed of light, with simple tools.
Safety Notes
- Do not overheat the chocolate or butter, as itcan burn.
- Hot chocolate and butter can cause skin burns.
- Do not place metal objects in the microwave.