VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The fundamental frequency for a tube will open at both ends is the wave speed which is the speed of sound since the thing that's resonating here is air inside the tube. And so the wave is moving through air which is a wave moving which is what sound is, a wave moving through air. So, we have v over 2 l and we'll solve for l, the length, we're multiplying by l over f1 on both sides. And we get l on the left equals v divided by 2 times the fundamental frequency on the right side so, that's l equals 331 plus 0.6 times the temperature over 2 f1, because this is the formula for the speed of sound as a function of temperature in Celsius degrees. So, we have 331 plus 0.6 times 22 degrees Celsius divided by 2 times 294 hertz which is a length of 0.585 meters. Now, if helium was inside the tube, the reason that helium makes a difference is because the speed of sound in helium is different. And table 12-1 tells us the speed of sound in helium at 20 degrees Celsius. And well that's close enough, I mean, we're working with 22 degrees but 20 is pretty close. So, we'll use the same figure because we don't have any formula to figure out the speed any other way. So, the length is going to be 1,005 meters per second divided by 2 times 294 hertz. And that's going to give a length of 1.71 meters would be required.