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## Class 9 Physics (India)

### Course: Class 9 Physics (India) > Unit 5

Lesson 3: Reflections, echoes, and reverberation# Minimum distance for echo

How far should an obstacle be to hear an echo? Created by Mahesh Shenoy.

## Want to join the conversation?

- A group of hikers hear an echo 8.66 seconds after they shout. If the air temperature is 10.9 degrees Celcius, how far away is the mountain that reflected the sound wave?(1 vote)
- The speed of sound at 10.9°C is approximately 337.78 m/s. The time taken for the sound wave to reach the mountain is 8.66 ÷ 2 = 4.33 s. Therefore, the distance between the hikers and the mountain is 4.33 × 337.78 = 1462.5874 m.(1 vote)

- Sir! is 17m specific for the echo to be heard? ANd time 0.1s is specific?

Like if I stand on a mountain the distance from that mountain and the other will be much larger. How will I hear an echo in less than 1 second when the distance is so large?(1 vote) - Perhaps should have asked this in the previous video, but are there other factors involved in how the echo is getting back to us? For instance, mountain ranges are comprised of geographical features that contain air in different amounts depending on the contour of the land they sit(?) in. If I'm in a desert and an object is 10 miles away, and I yell "yo", will I still get an echo from the object? Your videos are great by the way - thanks!(1 vote)

## Video transcript

- 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.