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

Sound travels in waves. These waves have both a frequency and an amplitude. The frequency is measured in hertz, which is one wave cycle per second. A cycle is a repeated pattern of positive and negative amplitudes. These cycles are repeated with a certain period, or time interval. This is why waves are called periodic functions. The amplitude is a measure of the height of the wave. Intensity is directly related to amplitude. Sound wave intensity is measured using a logarithmic scale with units of decibels. One bel is defined as the logarithm (base 10) of the ratio of two intensities. The scale is actually a ratio; the lower number is chosen arbitrarily. Zero decibels is set as the lower limit of our hearing. Bels are too large for most uses, so instead we use decibels (deci=1/10). The unit is named after Alexander Graham Bell, inventor of the telephone.

When waves interact, they don't reflect off each other--they combine. If the amplitudes of the waves are both positive or both negative, the combined wave will have a larger amplitude. This is called constructive interference. If the waves have opposite amplitudes, the resulting wave will have a smaller amplitude. This is called destructive interference.

Two waves that add together may have different frequencies. If this happens, at one point the waves will interfere constructively while later they will interfere destructively. These changes in constructive/destructive interference are also periodic functions. In music this is known as a wave beat. You can hear beats when two instruments are trying to play the same note but one is off by a little bit. Musicians use beats to help tune their instruments. Piano tuners will strike a tuning fork (which vibrates with a constant frequency) and then play a note on the piano. If they hear a beat, they know that they need to loosen or tighten 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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