Study Guide

Waves In the Real World

  • Engineering

    AM and FM Radio Waves

    While teams of frenzied German engineers are hard at work scaling an entire Bon Jovi cover band down to 3-Series console size for BMW, as of yet the radios in cars are just that—radio receivers. All that great music comes from nothing, plucked out of the ether by car antennas. If you've driven in a car since the early 1900s, chances are you probably know there are two kinds of radio that come over the air: AM and FM.

    On the surface it may seem like the only difference between the two types are the content—AM is all local news and Bach concertos, while FM is vulgar talk radio and top 40 songs—but in reality, these two technologies are entirely different ways to move sound from a studio to your ears. Both use radio waves, which have long wavelengths and low energy, and live at the very bottom of the electromagnetic spectrum under visible light and microwaves. However, the big differences come into play when we look at frequency. You know 101.2 The Edge that your brother listens to? Ever wonder where the 101.2 comes from? You know you're curious now...

    Each radio station has its own designated frequency to broadcast on. AM stations take up from 550 to 1700 kHz in 10 kHz increments (maybe you know an AM 680 or 1060 station?), while FM stations have much higher frequencies, ranging from 87.9 to 107.9 MHz in 0.2 MHz increments (here in the Bay Area Shmoop World Headquarters, we can listen to Live 105.3 or KLOS at 98.5). Any higher than that, and you move into microwave radiation—which runs the risk of cooking your car instead of feeding it great tunes.

    The two types of radio broadcasting technologies are named for the way they store and send information from a station to your radio. "AM" stands for amplitude modulation, while "FM" stands for frequency modulation—hopefully these terms ring a wave-related bell. In AM radio broadcasts, data is sent by changing the amplitude of the waves and keeping the frequency constant:


    And in FM radio, data is sent by changing the frequency slightly around the central band that shows up next to the station name, but keeping the amplitude constant:


    AM radio has been around longer and the signals can travel further, but FM radio is much less susceptible to interference and has gradually surpassed AM as the most-listened-to radio format. That is, until BMW miniaturizes that Bon Jovi band successfully.

  • Music

    Stringed and Piped Instruments

    All sound consists of pressure waves that travel through the air from their source to your ear. Some of these pressure waves are created in turn by standing waves—anything from a vibrating violin string to an oscillating pipe organ air column. When you pluck a guitar string, the string itself wobbles back and forth, pinched at each end, and this movement is what makes the sound wave that travels to your ear.

    However, most instrument standing waves do not just oscillate at one frequency. Instead, they produce many different frequencies at once. These different frequencies are integer multiples of the base frequency, called harmonics.

    From left to right: base wave with frequency fo, harmonic at 2fo, harmonic at 4fo

    For example, if a guitar string was tuned to play a middle A (a note with a frequency of exactly 440 Hz), it could also create sounds an octave above at 880 Hz or two octaves above at 1760 Hz. 9.

    The same thing happens in a pipe organ, though for pipes the position of the wave's nodes and antinodes are reversed:


    These harmonics combine together to create what human ears hear as a single note, and different combinations of harmonics can change the timbre of the sound, or even what note is heard.

    When a guitar maker goes to make an instrument, the sound the strings make is very much a science. We can find the resonant frequency of a string based on its mass m, length L, and the tension T it's held under.10 These three variables give us the velocity of the waves that interfere to form our standing wave:

    The resonant frequency of a string is given by dividing this value by twice the length of the string:

    So the frequency that the string vibrates at is only dependent on its length, mass, and tension. Of these three, mass and length are difficult to change on the fly—but tension is very easy to increase and decrease. That's why, whenever your guitar or violin or cello or ukelele gets out of tune, you can adjust the note each string makes by twisting the tuning knobs and either pulling the string more taute or adding slack. This changes T, which in turn changes fo and the sound of the string.

  • Astronomy

    The Doppler Effect, the Expanding Universe, and the Search for Exoplanets

    The words "Doppler Effect" get tossed around a lot by all sorts of people—highway patrol officers, TV weathermen, handsome physics education websites—but perhaps the people who toss it around with the most weight are astrophysicists and cosmologists. And no, this is not only because they sit around in their cubicles all day making WEEEE-OOOOOOOO noises with toy spaceships. Though that is a big part of it.

    Astrophysicists and cosmologists study the universe and the really, really big things floating around within it. And even though in space, no one can hear you scream, everyone can see you move—and that's how these space scientists use the Doppler Effect. They look not at sound waves, but at light waves, which experience the same kind of frequency shifting (admittedly without the race car noises).

    Recall in terrestrial applications of the Doppler Effect, sounds that are moving away from you sound lower, a decrease in frequency; sounds that are moving closer sound higher, an increase in frequency. The same thing happens with light—objects that are moving away appear redder (a decrease in frequency); objects that are moving closer appear bluer (an increase in frequency). 11 This phenomena was described for the first time in a seminal scientific treatise by Dr. Theophrastus Seuss entitled One Shift, Two Shift, Redshift, Blueshift.

    As scientists began noticing that light from stars seemed to be significantly redshifted—and increasingly redshifted as the stars got further away from earth—they realized that the entire universe must, in fact, be expanding.12 If the universe is expanding, it's a logical jump to assume at some point in time the universe was just that: a point. This, in a nutshell, is the Big Bang theory, which postulates that all matter in the entire universe once existed in a tiny point and expanded outward to fill the vast gulf of space we now inhabit. (Not to be confused with "The Big Bang Theory," a TV sitcom which postulates that one joke should expand to fill endless seasons of television.)

    While the idea of an ever-expanding universe may seem isolating if not a bit Lovecraftian, take heart—the Doppler Effect is also paramount in the quest to discover if humanity is alone in the galaxy or if there really are Wookiees out there waiting for us to find them. In the last few decades, humanity has discovered a number of extrasolar planets, or "exoplanets:" planets that orbit stars other than our own Sun. There are hundreds of billions of these planets in the Milky Way alone, with as many as 20% of those called habitable, meaning they are similar to Earth in size and distance from their star.13

    There are many ways to discover these planets, but one way is by using the Doppler Effect. As a planet orbits a star, it pulls on the star with its own force of gravity—remember Newton's laws?—and this moves the star a tiny bit as the planet flies around. This star movement is enough to shift the light coming from the star, which tips off astronomers that the star has a planet circling it. If this seems like it might be hard to discern, well, four hundred and fifty-six exoplanets disagree.

    The universe may be expanding, but the Doppler Effect has also shown it's a bit more crowded than we thought. There's hope for finding those Wookiees yet, and there will be a substantial reward for the one who does. But we want them alive—no disintegrations!