A flutist assembles her flute in a room where the speed of sound is 342 m/s . When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to where the speed of sound is 346 m/s. b. How far does she need to extend the 'tuning joint' of her flute to be in tune with the tuning fork?

Video transcript

Hey, everyone. So this problem is dealing with open open air columns. Let's see what it's asking us. A musician adjusts the length of his instrument to produce a fundamental frequency of exactly Hertz on a day when the speed of sound in the air was 343 m per second. But the concert was held on a different day when the speed of sound was only 338 m per second. How much should the musician ad adjust the length of his musical instrument, which is an open open air column to obtain the same frequency. And so our multiple choice answers are if the length should be decreased by 5. millimeters or 1.8 millimeters, or if the length should be increased by 1.8 millimeters or 5.1 millimeters. So the first thing that we can due for this problem is recalled that the frequency in an open open two is given by the equation F equals N V divided by two L. And we're told that it's the fundamental frequency. So we know that N equals one solving for and substituting one for N, we have L equals B divided by two F. So on that first day, we can solve for the length of this instrument. So we call that the initial length. So the speed of sound was 343 m per second, divided by two, multiplied by our frequency Hertz. We plug that in and we get a length of 0.3472 m. Now the day of the concert, we'll call that our final place. The speed was decreased to 338 m per second. And our frequency is the same as the goal, right? What length do we need to get the same frequency? So that's 494 Hertz and he gets 0. m. And so the final step is just going to be to subtract our initial length from our final length and we get negative 5.1 millimeters. And so it's negative. That means it should be decreasing, the length should be decreasing by 5.1 million years. And that aligns with answer choice A so that's all we have for this one. We'll see you in the next video.