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Have you ever been in a place that was so noisy that ordinary conversation was impossible? Imagine being the pilot of a plane or the engineer on a locomotive where loud engine noise is a constant, irritating presence. Over the past few decades advances in electronics and miniaturization have made it possible to eliminate constant background noise while allowing voices and other sounds to pass through! This technology is called active noise cancellation and it is based on the destructive interference of sound waves. 
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The sounds of everyday life are made up of hundreds or thousands of different frequencies all superposed on top of each other. Although the human ear can separate out different frequencies, sometimes background noises become so loud that it is impossible to hear the desired sounds—such as someone’s voice or music.
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In many cases the information you want to hear, such as a voice, has the following characteristics: - The amplitude changes relatively quickly, on time scales of a second or less and
- most of the information is carried in frequencies higher than a few hundred hertz.
A background noise, such as a loud hum from an engine, has different characteristics:
- The amplitude is relatively constant over time scales of 10 s or so and
- the frequencies are low, typically less than a few hundred hertz.
Active noise cancellation uses the differences between these two kinds of sounds to interfere destructively with one while leaving the other unchanged.
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Active noise cancellation technology is now used to improve safety for pilots, train conductors, and workers in noisy areas, but it has also appeared in cellphones, cars, and home stereo headphones. You may not even know that your cellphone uses antinoise to cancel out the sound of wind or other low-frequency noise from your phone calls. Many high-end cars include a “black noise” system, which uses internal microphones and special speakers to actively cancel tire and road noise from the interior of the car.
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Any noise-canceling technology includes a microphone that samples the external noises that you want to cancel out. In noise-canceling headphones, each earphone contains one or more small microphones located on the outside. The microphones are connected to a powerful computer chip that drives a miniature amplifier. The amplifier drives a speaker inside the headphones. This internal speaker can send sound directly into your ear.
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Noise-canceling headphones use destructive interference. Which of the following explains destructive interference? - harmonic motion
- the spectrogram
- Fourier’s theorem
- the superposition principle
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The correct answer is d. The superposition principle states that the total amplitude at any instant of a wave made up of multiple waves is found by adding up the independent amplitudes of the individual waves. This explains how waves interfere with each other, including constructive and destructive interference. 
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