(a) Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern that has the same frequency as the note that is sung. If someone sings the note B flat, which has a frequency of 466 Hz, how much time does it take the person's vocal cords to vibrate through one complete cycle, and what is the angular frequency of the cords?

Question

Accepted Answer

Hey everyone welcome back in this problem. We're told that vibrating objects emit sound that matches their vibrating frequency In music. The frequency is categorized into notes. So a keyboardist is playing C. sharp a note with a frequency of 554 Hz. The sound is emitted by the diaphragm in a speaker that vibrates at this frequency and were asked to determine the time taken by the diaphragm to complete one cycle and its angular frequency. Alright, so let's start with the first part. We want the time taken to complete one cycle. Well what does that sound like the time taken To complete one cycle? Recall that this is just the period. We can write it as t. Okay, so time taken to complete one cycle. That is the definition of the period. So what it's asking us to do is find the period. Now we're given a frequency, we want to find a period recall that those are related through the inverse. Okay, so the period is going to be one over the frequency F. Which is one over 554 Hz. Which gives us a value of 0. approximately seconds. Okay. And if we write this in scientific notation we can write this as 1.8, 1 times 10 To the - seconds. Alright, so we found our period here. Now moving to the second thing it's asking is the angular frequency and the angular frequency is given by omega and recall that omega is equal to two pi times the frequency F again. We know the frequency F ever given in the problem. So we can go ahead and calculate this two pi times 554 hertz. And this is going to give us an angular frequency of 3,480. in our unit here is radiant per second. Because we have this pi radiance times hurts get radiant per second And writing this in scientific notation 3.48 times 10 to the three radiance per second. Okay. With three significant digits there. And so if we look at our answer choices, we found that the period is 1.81 times 10 to the negative three seconds and the angular frequency is 3. times 10 to the three radiance per second. And so we have answer choice. D. Thanks everyone for watching. I hope this video helped see you in the next one.

Verified Solution

Key Concepts

Frequency

Time Period

Angular Frequency