During World War II, two scientists invented the magnetron, a tube that produces microwaves. Installing magnetrons in Britain’s radar system, the microwaves were able to spot Nazi warplanes on their way to bomb the British Isles…. The idea of using microwave energy to cook food was accidentally discovered by Percy LeBaron Spencer of the Raytheon Company when he found that radar waves had melted a candy bar in his pocket. Experiments showed that microwave heating could raise the internal temperature of many foods far more rapidly than a conventional oven.

So, what exactly is a microwave, and are microwave ovens safe? We’ll need to consider the electromagnetic spectrum, something you’ve probably seen in your high school physics and chemistry classes.

The Electromagnetic Spectrum

Put simply, a “micro”-wave is a “small” wave that is on the order of 1 centimeter, not on the order of 1 micrometer, as the name would suggest. That is, these waves have wavelengths of about 1 centimeter. (A centimeter, or cm, is 1E-2 m.) When we compare this with visible light, which is on the order between 1E-6 and 1E-7, we see that microwaves are longer than visible light. If we remember that speed of light = (frequency of the wave)*(wavelength of the wave), where the speed of light is about 2.9979E8 m/s, then we can see that frequency is inversely proportional to the wavelength. What this means is microwaves travel at a lower frequency than visible light. (Frequency is measured in cycles per second, or Hertz.)

Again, from IdeaFinder.com:

[Microwaves] are found in the non-ionizing portion of the energy spectrum, between radio waves and visible light. “Non-ionizing” means that microwaves do not detach charged particles and produce atoms with an unbalanced plus or minus charge. Microwaves can therefore safely produce heat and not cause food to become radioactive.

Now, let’s take a look at a few practical things about microwave ovens, like why radiation doesn’t escape into the kitchen, or is it safe to stop the microwave and reach in to grab the piping hot HotPocket about eat it right away? If you notice that there is a metal mesh screen in the door of the microwave. The side of the holes, on the order of half a centimeter or so, allows the physically smaller visible light waves to pass through but prevents the “larger” microwaves from leaving the microwave oven (remember that light waves are orders of magnitude smaller than microwaves). Also, you don’t need to worry about residual microwave radiation from the microwave oven because these waves always travel at the speed of light and will have been absorbed into your food long before it gets a chance to escape and hit you in the face.

More information on the history of the microwave oven can be found at Gallawa.com. Image from ScienceProg.

When you pluck a guitar string, you are essentially inducing what is known as a standing wave on the string. The plucked string is fixed at both ends, while the middle oscillates up and down very quickly, resulting in what looks like a standing oval along the string. Therefore, the term “standing wave” is aptly and intuitively named. In this particular case where the standing wave looks like one oval (not two or three, etc.), the wavelength of the standing wave is simply twice the length of the “oval.”

Standing waves on guitar strings look sort of like single ovals.

To understand how you can get different tones of sound from one guitar string, we need to understand how sound and wavelength of the standing wave are related. One basic relation in mechanics is that speed equals the product of wavelength and frequency. We can apply that to sound: the speed of sound equals the wavelength times the frequency of oscillations of the vibrating object. The vibrating object in this case is the plucked guitar string. We can assume that the speed of sound in air is constant (the speed of sound is different in other media, such as water), so essentially the wavelength and frequency of the standing waves are inversely proportional – a short wavelength leads to a high frequency, and vice versa.

Now, where does the actual sound that we hear come in? The induced frequency from the standing wave’s wavelength gives rise to the sound that we hear. As long as there is an active wave on the guitar string (meaning the string is moving due to plucking and not just sitting there doing nothing), there is an associated wavelength and therefore a frequency as well. High-pitched sounds have high frequencies, and low-pitched sounds have low frequencies. Therefore, to get a high-pitched high-frequency sound from a guitar string, you want to fix one end of the string with your finger so that the wavelength is short, and this happens to be the part of the fingerboard closest to where your plucking fingers are. Using the same logic, you can get a variety of pitches by fixing the string’s end at various locations while plucking, which is exactly what guitar players do.

This is how you get different pitches of sound from one guitar string. There are other interesting aspects of musical instrument design, such as why different guitar strings have different pitches themselves, and how wind instruments (such as flutes) work.