Two strings are adjusted to vibrate at exactly 200 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at the same time. What is the new frequency of the string that was tightened?

Video transcript

Hey, everyone. So this problem is working with beat frequency. Let's see what it's asking us musicians often tune their instruments before a performance to ensure accurate pitch. Suppose a guitarist tunes his instrument by adjusting two strings to oscillate precisely at 250 Hertz later, he notices that one of the strings is slightly out of tune and increases its tension. This change results in four beats per second being audible when the two strings vibrate simultaneously determine the new frequency of the string with the increased tension. And our multiple choice answers here are a 254 Hertz B 344 Hertz C 220 Hertz or D 328 Hertz. OK. So this is a very straightforward problem as long as we can remember that the beat frequency is given by the frequency of our beat is equal to F one minus F two. And so because the tension is increasing, we know that the frequency is increasing, which means we are finding the larger of the two frequencies here or F one. So F one is equal to F eight plus F two and F beat was given to us four beats per second is that frequency of the beat. So that's four hertz. And then our initial uh frequency was hertz. So that new frequency is 254 hertz. And that's it that aligns with answer choice. A pretty straightforward. I will see you in the next video.