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Two waves of slightly different frequency create beats when added together.
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Wave Beats

Sound travels in waves. You hear sound because waves hit your ear. Sound waves are similar to ocean waves. They both have a certain frequency. The frequency is measured in hertz, which is one cycle per second. One wave cycle is a complete wave; both the up half (crest) and down half (trough) are part of one cycle. People can hear sounds between 20 and 20,000 hertz. Waves also have a certain amplitude. Amplitude is a measure of how strong the wave is; the higher the amplitude, the higher the crests and deeper the troughs. The amplitude switches between positive and negative during each cycle. Waves are called periodic functions because they repeat in a certain period, or time. Period and frequency are related.

Waves don't usually reflect when they strike other waves. Instead, they combine. If the amplitudes of two waves have the same sign (either both positive or both negative), they will add together to form a wave with a larger amplitude. This is called constructive interference. If the two amplitudes have opposite signs, they will subtract to form a combined wave with a lower amplitude. This is called destructive interference. Sound waves with higher amplitudes sound louder than sound waves with lower amplitudes. Constructive interference will make a sound louder while destructive interference will make a sound quieter.

Two waves that add together may have different frequencies. That means that the crests and troughs won't add up the same way with each new wave because one is moving faster than the other. Part of the waves will interfere constructively and part will interfere destructively. This is known as a beat in music. You can hear beats when two instruments are almost playing the same note but are not quite together. Musicians use beats to tune instruments. Piano tuners strike a tuning fork and then play a note on a piano. If they hear a beat then they know they need to tighten or loosen the string for that note. When the beat disappears, the note is in tune. This is how Doppler could tell that the frequency of the trumpets on the moving train had changed--he could hear the wave beat.

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