The wings of the blue-throated hummingbird (Lampornis clemenciae), which inhabits Mexico and the southwestern United States, beat at a rate of up to 900 times per minute. Calculate (a) the period of vibration of this bird's wings, (b) the frequency of the wings' vibration, and (c) the angular frequency of the bird's wing beats.

Video transcript

Everyone in this problem we're told that bees flap their wings at a rate of 13,800 beats per minute. And were asked to determine the period T. The frequency F. And the angular frequency omega for the flapping of a bee's wings. All right now when we're giving this rate of their wings flapping a 13,800 beats per minute. Okay this is actually a frequency. Okay. And so we can write the frequency f. This is gonna be 13,800 beats per minute. And we want to write this in units of hurts. Okay So we want to convert this minute into seconds. So we can multiply and we have one minute Her seconds. The unit of minute will divide. And we're going to be left with 13,800 per seconds. Which gives us a frequency of 230 hertz. Okay. Alright so that rate were given beats per minute. That is a frequency and we just needed to convert the units. Okay. Alright so we have our frequency 230 hertz. Okay now let's move to the period. Okay And let's recall that the period T. Is related to the frequency through the inverse. So the period T. Is equal to one over the frequency F. Okay so this is going to be equal to 1/ Hz. Okay and this is equal to 4. times 10 To the -3 seconds. Alright so we found our frequency F. We found our period T. The last thing we need to find is the angular frequency omega. Okay. Alright. Now let's recall that we can write the angular frequency Omega is equal to two pi in terms of frequency app. Well this is gonna be equal to two pi times the frequency we found was 230 Hz. And this is going to give an angular frequency of 1.45 Times to the three radiance per second. All right, so, we have the three values we were looking for there. We look at our answer choices and we found a frequency of 230 hertz. So we're looking at answer choice. Either ear F. Okay. We found a period of 4.35 times 10 to the negative three seconds. And an angular frequency of 1.45 times 10 to the three radiance per second. So, we have answered e. Thanks everyone for watching. I hope this video helped see you in the next one.