Interference
Interference is something that happens with all kinds of waves: electromagnetic waves, sound waves, water waves. The key to understanding it is the PRINCIPLE OF SUPERPOSITION: Where two waves overlap, the total disturbance at that point and time is the sum of the disturbances from the two waves. We say that the two waves interfere with each other, producing an interference pattern. If the two waves make a bigger wave, we say there is constructive interference. If the two waves partially or totally cancel each other out, producing a smaller wave, that is destructive interference. The two graphs below illustrate these: the light lines (one solid, one dashed) are two waves. The thick line shows the point-by-point sum of those two waves.
Open this spreadsheet that allows you to animate the constructive and destructive interference of two waves. Scroll to the right a little and use the left-arrow and right-arrow buttons to move the waves pulses and observe what happens. (If Excel gives you a security warning that "Some active content has been disabled", go ahead and authorize it to "Enable this content.")
Imagine we have two point sources of waves. Two rocks thrown simultaneously into a pond, for example. The ripples spread outwards. Where crest meets crest and trough meets trough, we have constructive interference (a big wave). Where crest meets trough, there is destructive interference and the water is flat and still. What you get is a moiré pattern on the water. The diagram shows two sets of circular ripples (crests) overlapping each other.
BEATS are caused by the interference of two waves with slightly different wavelengths, causing a pattern of alternating constructive and destructive interference. Two waves are shown in the left-hand diagram below. Two waves that start out in phase become out of phase in a short distance, because one has a shorter wavelength. The middle diagram shows the sum of those two waves: near zero on the x-axis the waves constructively interfere; near x=5 they are destructively interfering. The right-hand diagram shows the same pattern, only zoomed out a bit. The whole pattern of waves with increasing and decreasing amplitudes moves much as the individual waves do. If these are sound waves (the most common example of beats) you hear the tone of the individual notes, but also a "warble" or throbbing sound. The loudness (amplitude) is varying: the frequency of this warble is called the beat frequency. If the two individual waves have frequencies f1 and f2, then the beat frequency is
Play with this spreadsheet illustrating
beats. (If Excel gives you a security warning that "Some active content has been disabled", go ahead and authorize it to "Enable this content.") Before changing anything, notice that the two waves (in thin black
and red lines) are out of phase at the left edge, causing destructive interference.
The yellow line shows the resulting wave, of low amplitude. The two waves
have slightly different wavelengths, so by the right-hand edge, the two
waves
are in-phase,
creating
constructive
interference.
Now,
advance the time by pressing the right-facing arrow button.
Click the thumbnail below to start a video showing (and playing) audio tones to create beats.
Examples from everyday life: tuning a guitar or piano, jet engines
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ELECTRONIC NOISE CANCELLATION: Exposure to loud noises can permanently damage your hearing. Such damage is cumulative, because the hair cells in your inner ear, the ones that actually sense sound, cannot repair themselves. So a little damage here and a little there adds up. That's why older folks are often hard of hearing. You can prevent this from happening to you by wearing hearing protectors or earplugs when in a loud environment. These protect your ears by blocking most of the sound waves from getting into your ears. The disadvantage of wearing them is it's hard to hear low-level sounds, like someone talking to you. Nowadays, there are new electronic hearing protectors that work on a totally different principle. Instead of merely blocking sound from reaching your ears, these electronic headsets have built-in microphones and small speakers. The microphone detects the incoming sound waves, and the speakers produce another sound wave that is always out of phase with it. The two waves destructively interfere. This is called electronic noise cancellation or active noise cancellation. The headset pictured to the right is one model, called the NoiseBuster by Pro Tech Technologies, Inc. |
Activities & Practice
to do as you read
1. Here is one of the simulations that we played with when we first talked about waves. Turn on the "Two Drips" option and observe the resulting interference pattern. Notice that there are places in the sink where the water is NOT moving up and down. These are locations of destructive interference. Use the "Add Detector" button to place a wave sensor in various spots.
Additional Activities & Practice
2. You have two tuning forks, both of which are supposed to have a
frequency of 512 Hz. But when you strike them simultaneously, you
hear a 3-Hz beat. Assuming
one of the forks is in tune, what is the frequency of the other fork?
3. When flying on a jet airplane you hear the engines, of course. Much of an engine's noise is at the same frequency as the spinning frequency of the turbine. In other words, if the turbine is spinning 150 times per second, there will be lots of 150-HZ sound. If you are on a twin-engine plane, and if one engine is spinning a little faster than the other, their combined sound will seem to throb. Suppose you are on such an airplane, and there are two throbs (beats) per second. By how many rpm (revolutions per minute) is one engine running faster than the other?