A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?

Video transcript

Welcome back, everyone. We are making observations about a self-driving drone and we are told that it navigates in space by emitting sound waves. And we are told that the frequency of the sound waves that it emits are kilohertz or 22 times 10 to the third hertz. And we are told that it detects a reflected frequency of 18 times 10 to the third Hertz. And we are tasked with finding the magnitude and direction of the drone's velocity. Well, we know that the drone is altered by the Doppler effect so we can apply the same laws and rules. And since our reflected frequency is lower than the initially emitted frequency, we know that the drone is moving away from whatever object reflected the wave. So what are we going to do here? Well, here's what we can do. We can say that our reflected frequency is equal to the initially emitted frequency divided by one plus the velocity of the drone divided by the speed of sound through air. And what I'm gonna do is I'm gonna divide both sides by our initially emitted frequency and then I will flip both sides of the equation. What we will have is that the velocity of our drone divided by the velocity of sound through air plus one is equal to our initially emitted frequency divided by the reflected frequency. I will now subtract one from both sides. And then I can multiply both sides by our velocity of sound through air. What we get is that the velocity of our drone is equal to V times F over F R minus one. Let's plug in some values for this. We have that the velocity of sound through air is 3 43 m per second. It's gonna be multiplied by 22 times 10 to the third, divided by 18 times 10 to the third minus one. And what this gives us is 76.2 m per second away from the object that caused the reflection, which corresponds to our final answer. Choice of C Thank you all so much for watching. I hope this video helped. We will see you all in the next one.