A string under tension has a fundamental frequency of 220 Hz. What is the fundamental frequency if the tension is doubled?

Video transcript

Hey, everyone. So this problem is dealing with frequency and tension. Let's see what it's asking us when a plastic line of length L stretched to attention of T between two plants. The frequency of the first harmonic is Hertz. The tension is tripled by turning the clamps calculate the new frequency of the first harmonic. Our multiple choice answers are a 1.4 times 10 to the two Hertz B 3.3 times 10 to the two Hertz C 5.8 times 10 to the two Hertz or D 6.3 times 10 to the two Hertz. So the two key equations that we need to recall for this problem are the frequency is equal to the speed or V divided by the wavelength or lambda. And in turn, speed is equal to the square root of tension divided by new. So for that first or that we can call it the initial or that first scenario before the clamps are turned, we'll have F one is equal to V one divided by lambda. And the second, you can say very similarly, F two is equal to B two divided by lambda. So our speeds are going to change when the tension changes. But our wavelengths will not our speed V one is simply equal to the square root of T divided by mu V two is equal to the squared of three T divided by mule. And we can split up that squared of three and say V two is equal to the squared of three multiplied by V one. So now we can solve for F two as a function of F one. So F two is equal to squared of three multiplied by V one divided by lambda where V one divided by Lambda is F one. So F two is going to equal square to three multiplied by F one or squared of three times 190 sorry squared of three multiplied by 192 Hertz. When we plug that in to our calculator, we get 3.3 times 10 to the two parts. So that is the answer to this problem. And that aligns with answer choice fee. That's all we have for this one. We'll see you in the next video.