Standing Wave On A Guitar

by Patrick Ford
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Hey, guys, let's do an example. Ah, guitars played by plucking the string, which emits a sound at the frequency it vibrates to play different tunes. The string is held down by your finger at what are called fret locations. Each subsequent fret, shortening the length of the string by about two centimeters. If a guitar string has a full length of 64 centimeters and attention of 70 Newton's in a mass sprint length of one times 10 to the negative kg per meter. What is the frequency emitted by the guitar if held at the 10th Fret location? Okay, so remember, the string starts out at 64 centimeters, and each fret shortens the length of the string by about two centimeters. So if you're at the 10th fret, that means that you're at minus 20 centimeters for the length. So the new effective length, which all called El Prime, is 64 centimeters minus centimeters, which is 44 centimeters. So you're actually playing a string that's Onley 44 centimeters long because you are holding one end of the string down to shorten the total length of the string. Now the string is fixed at both ends. So this is a node node standing wave right. Which means that the frequency is going to be in times V over two times our new length, not the 64 centimeters, because when you're holding out of the 10 Threat, you've effectively shorten the length of the guitar. The question is, what mode are we in? What harmonic number? Well, if the guitar string is fixed at both ends and you pluck it, what happens is it vibrates like this up and down. Okay, this is in equals one. Alright. And that's all we need. So the frequency it's gonna be v over two times the new length. Alright, that speed, we don't quite know, but we know enough to solve for it, right? The speed is the square root of the tension which is 70 divided by the mass per unit length which is one times 10 to the negative three, which is Sorry, 265 meters per second. Couldn't read my notes for a second 265 m per second. So this is going to be 265 m per second, divided by two times our new length, which is 44 centimeters or 44 which is going to be about 301 hurts. That's gonna be about the frequency emitted by the guitar. Alright, guys, that wraps up this problem. Thanks for watching.