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QUick easy astronomy and physics type questions. thank you

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Rowan Introduction to Astronomy Activity #5: Microwave Ovens & Speed of Light Name: _______________________________________________ Score: _________________________________ Using Marshmallows to Determine the Speed of Light [40 pts] When we talk about the speed of light, we typically think of visible light. Though physicists have performed experiments that demonstrate the speed of visible light, the equipment required is too complex and expensive for most individuals to have in their homes. Because the speed of light is a fundamental constant, all electromagnetic radiation—including visible light—travels at the speed of light: c = 3 × 10 8 m/s. Most of us have access to a microwave oven that produces microwaves—another form of electromagnetic radiation. Conveniently, consumer-style microwaves have a wavelength that is macroscopic in size, i.e., we could measure the wavelength of these microwaves with a standard centimeter rule if we could see the waves. There is a way for us to “see” these microwaves and to measure their wavelength. If we take a plate of marshmallows and microwave them for about 30 seconds, we will observe that some of the marshmallows are melted (at least partially) while others appear to show minimal heating. By measuring the distance between the melted marshmallows—the “hot spots”—we can determine the speed of light. The microwaves generated in a microwave oven are often said to bounce around within the oven’s interior. Actually, the microwaves generated by the appliance very quickly form standing waves inside the cavity where you put food. In many microwave ovens, the food is placed on a rotating dish. As the food rotates around, it passes through the standing wave nodes, and the intensity of radiation at those points excites the water molecules in the food and the food is heated evenly. For this experiment, the rotating dish must be removed. We want the hot spots created in the plate of marshmallows to remain so that we can measure the distance between those hot spots. Once the marshmallows are heated, we can take our ruler and measure the distance between the melted parts of the marshmallows. One should find that there is an even pattern of melting and that the distance between the hot spots is approximately 6 cm. That measured distance is the distance between the nodes of the standing waves. The melted marshmallows represent a “map” of the standing wave pattern of the microwave oven. The distance between the melted sections of the marshmallow is in fact λ/2, because there are two nodes for each standing wave. From our measurement, we know that λ/2 = 6 cm. The frequency of the microwave oven is written on the manufacturer’s plate on the back of the oven. The typical frequency for a consumer-style microwave oven is 2450 MHz (megahertz). We use the formula velocity = frequency times wavelength: v = × λ. Knowing the wavelength and the frequency, calculate the speed of the microwaves (which is the same as the speed of light). Plate of marshmallows inside of a microwave oven. Microwaved marshmallows show the pattern of the standing waves in the oven. Measuring the distance between the hot spots gives one-half the wavelength.
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