There are four general categories of musical instruments: guitars and pianos are examples of vibrational strings, trombones and flutes are examples of the open-and air column instruments, organ pipes are examples of the closed-end air instruments, and drums are examples of vibrational mechanical instruments.


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Mathematically speaking, guitar strings are easy to do calculations because the natural frequencies that the strings vibrate at depend on only the tension, length, and what the string is made out of. Here is how you do it:


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When you blow into the mouthpiece of an instrument, the vibrations create frequencies, and the ones that resonate with the air in the tube inside the instrument are the ones you hear as a loud sound. When an instrument is open at both ends, it’s called an open-end air column. Here’s how to figure out the frequencies of these types of instruments:


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Let’s take a real example of a musician playing a flute:


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Have you ever blown across a glass bottle? If so, you’ve played one of these instruments! Pipe organs are also closed-end air instruments because one end is sealed. The difference in sealing one end affects the types of frequencies that the instrument can create because the standing wave pattern that is created is from the incident (incoming) waves interfering with the reflected waves bouncing back when they hit the sealed end of the instrument.


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Have you ever put a cardboard tube up to your ear? What you hear depends on whether the tube is right up against your ear or offset so there’s a space between your head and the tube, because it goes from being a closed end to an open end air column, which changes the standing wave pattern inside. Here’s how to figure it out:


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Once upon a time, people used record players to hear music. Records were these big black discs that played on a machine. Spinning between 33 and 45 times per minute on a turntable, people used to listened to music just like this for nearly a century.


Edison, who had trouble hearing, used to bite down hard on the side of his wooden record player (called a phonograph) and “hear” the music as it vibrated his jaw.


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