Minimum distance for echo

- Imagine you're standing in front of an obstacle. The question we are going to try to answer in this video, is what must be the minimum distance, between you and the obstacle for you to hear an echo. Now at first you may be like, wait a second, why should there be a minimum distance to hear an echo? So, let's first understand what the question is before we try and answer it. So, let's take an example. Imagine you shout "Yo!" and that sound will go hit the rock and reflect back towards you and you might hear an echo. But here's the thing, we've seen in a previous video that in order to hear a distinct echo the time gap between the original sound and the reflected sound must at least be .1 second. So, you see if the obstacles are very close to us then you hear the reflection very quickly. Less than .1 second. And your brain cannot distinguish between the original sound and the reflected sound and as a result we'll hear both the sounds together as one single sound and we won't hear an echo. But, if the obstacle is far away such that the reflected sound reaches you after .1 seconds then your brain can tell between the original sound and the reflected sound. And as a result we can hear a distinct echo. And if you need more clarity on this then we have spoken a lot about it and we have done a demonstration in a previous video. So it would be a good idea to go back, watch that video and then come back over here. But anyways, now hopefully we understand why there must be a minimum distance. A minimum distance is needed so that the sound spends enough time in the air before reflecting and coming towards you so that we can hear the distinct echo. And so the question is, what is that minimum distance? So let's try to solve this. Let's say that the minimum distance between you and that obstacle is d. So D is that minimum distance, let's say. Then what do we know? Well, we know that if the obstacle is at the minimum distance the time taken by the sound to hit that obstacle and come back to you must be exactly .1 second. Right? That's why if the obstacle is closer, the time taken will be smaller and we won't hear the echo. But if the obstacle is farther, then the time taken will be larger than .1 second and we will be able to hear the echo. And so at the minimum distance the time taken must be exactly .1 second. So we know that time taken by the sound to come back. We also know the speed of sound. The speed of sound in air is pretty close to 340 meters per second. Now of course this speed does depend on a lot of things like, it depends upon the breeze and depends upon the medium like whether its air or water. It also depends on the temperature, but at normal temperatures in air the speed of sound is close to this number. So we know the speed of sound. And so, knowing the speed and the time for which the sound is spending in the air, can we calculate the value of d? How do we do this? Well we know one connection between speed, time and distance. And that connection is speed equals distance over time. And so maybe we can use this formula and substitute the numbers and find the value of d. So, you know what, it'll be great idea to first see if you can try this yourself. So go ahead, pause the video. Take a pen and paper and see if you can do this on yourself first. All right, let's do this. So let's plug in. We know the speed of sound is 340 meters per second, so the speed of sound is 340 meters per second. That equals distance divided by time. We know time, let's put that first. The time is .1 second. And what's the distance? Well you might think distance is d, but its not. You see, the sound has to go forward and then come back to hear the echo. So the total distance traveled by the sound is two times the value of d. So it will be two d. It makes sense, right? This .1 second is the time for which the sound is going forward and backward. And so the total distance has to be two d. And if you look carefully, from here onwards we just have to figure out what d is. That means all we have to do is algebra. And so, again, if you couldn't do it before, great idea to try to do the algebra from here onwards and see if you can calculate the value of d. So again, pause the video and see if you can do this. All right, let's do it. So since I want to calculate what d is let me first get rid of the denominator. To do that, I multiply by .1 second on both sides. .1 seconds here, .1 seconds over here. And so the .1 seconds divides out on the right and over here the second divides out. So what do we have? Well on the left hand side we have 340 into .1. 340 into .1 is 34. So that will be 34 and there is a meter over here. And on the right hand side we have two d. Now to calculate what d is, I want to get rid of this two. So to do that I am going to divide now by two on both sides. And so the two cancels and what we are left with is 34 by two. That is 17 meters. That equals d. And there's our answer. So this means that the minimum distance the obstacle needs to be at to hear an echo is 17 meters. So if the obstacles are closer than 17 meters, we won't hear the echo. And so this explains why we don't hear echoes in our rooms. That's just because the walls and the ceilings, basically anything that can reflect sound is much closer than 17 meters. But if you go at the mountains you have open space and the mountains are very far away. Much farther than 17 meters and that's why we can hear echoes usually at the mountains. And so what did we learn in the video? Well we learned how to calculate the minimum distance to hear an echo. To do that, we need to remember one thing. That the time gap between the original sound and the reflected sound must be at least .1 second. Then all we have to do is use the formula speed equals distance by time and with that we could calculate the value of that minimum distance.