Have you ever wondered how far away the lightning
was or where the lightning struck?
Is it possible to know the distance between
the lightning and your location just by counting?
It is.
In this first video of mine, I will teach you how to find out the distance between the
lightning and your location just by counting.
Let's start.
 
 
 
 
 
 
 
For instance, the lightning struck in a specific location.
 
 
While you stood in here.
 
 
 
You wanna know how far the lightning is from your place.
 
 
 
 
 
But what is lightning?
Lightning is the flow
of high voltage electric current.
High voltage means high temperature.
 
High temperature results
in the expansion of air where the lightning struck.
In the expansion of air, shock waves occur.
This is how sound is created which is called thunder.
In simpler terms,
When this phenomenon occurs, you see light.
The light you see is called the lightning.
 
 
When this occurs, sound is produced.
This sound is called the thunder.
How do you find out how far the lightning is from your location?
What you can do is, by definition of speed,
speed equals distance over time
We can estimate the distance the soundwaves traveled from the lightning location to you.
Therefore
Distance equals speed x time.
 
But what is the speed of sound?
The standard speed of sound is 343 m/s.
Take note that sound travels through a medium.
In this case, the sound travels through vibration in the air.
But not  just air, but air at specific temperature which is 23 degree Celsius with this speed 343 m/s.
This is the standard speed of sound in air
at 23 degree Celsius.
This means, I now have speed,
I just have to find the time the
sound travelled from the lightning location to my ears.
If in case you don't have a stopwatch
on hand,
you can still estimate the time it took for soundwave to travel.
How's that?
You just have
to count, but not simple counting like 1,2,3.
What you’ll do is to insert a word after
each number. For example 1,000; 2,000; 3,000. Because while you’re saying this phrase, this is equivalent to 1 second.
Instead of using stopwatch you can count.
For instance,
once you saw the lightning, start counting.
So, 1,000; 2,000; 3,000 then you heard the
sound,
that means the time consumed from the lightning location to yours is 3 seconds.
This means I now have time, and speed.
Now I can find the distance between me and where the lightning struck.
Once again, distance
is equals speed x sound. Standard speed of
sound is 343 m/s. Multiply it to time which
3 secs. Unit analysis, therefore the distance
is 1,029 meters. This means, the distance
is approximately 1 km. That’s how simple
it is--you simply count 1,000; 2,000; 3,000
til you hear the thunder from the time you
see the lightning then multiply it to 343
m/s. That's how easy it is to find the distance
between the lightning and your location. Now
let's try to experiment.
Let’s go.
So I’m in the back of our house; in a private
road, what we’ll do is to conduct an experiment,
but of course it's hard to experiment with
a lightning. So what we'll do is use an alternative.
If you can see it, there's a car using hazard
lights. What the driver will do is to use
the high beam and honk the car horn simultaneously.
Once we see the light, we’ll start counting
until such time we hear the car horn. Then
we'll compute for the distance. To confirm
the accuracy of our counting, we’ll do it
with a stopwatch.
So it’s almost 2 seconds. In this stopwatch
you’ll see the time at which my sister stopped
the clock. Based on our experiment, what we
calculated was approx 2 seconds. In short,
we can now know how far the car is from us.
Now I can compute for it. Therefore, distance
= speed of sound x time. Like I said earlier,
speed of sound is 343 m/s x time which is
2 seconds. Therefore, the car's distance from
us is approx 686 meters. Now let's look at
the google maps to see how far the distance
was. Based on google maps, the actual distance
is 700 meters. Very close to our computation.
Now question, what is the reason behind the
discrepancy of our computation? The reason
is the speed of sound we used which is 343
m--this is the speed of sound in air with
23 deg celsius temperature, standard. When
I checked the temperature, the temp was 28
deg celsius. Take note the speed of sound
in gas depends on the temp of gas. This means
that 343 is not applicable. Now what is the
derived formula for the speed of sound at
any gas, at any temp? You can check the derivation
of this formula at the description below.
But I'll just write it here. So speed of sound
at any gas is square root of kRT. Let’s
enumerate those variables. First, the capital
T is the absolute temp in kelvin, which is
equal to temp in celsius, just add 273 to
convert it to kelvin. Now what is R? R is
specific gas constant, which is equal to 287
joules per kilogram kelvin for the air. Now
what is the small letter k? K is specific
heat ratio, which is equal to specific heat
ratio at constant pressure divide specific
heat at constant volume which is equal to
1.4 which is for air standard. That's the
speed of sound at any gas at any temp.
This means the speed of sound we will compute,
considering the temp during the experiment,
28 degree celsius, will be sq rt of 1.4.
k of air x r of air which is 287 joules per
kilogram kelvin x absolute temp (28 + 273
to convert to kelvin).
Cancel this.
Maybe someone will ask, how will the sq root
of the remaining unit (sq rt of joules/kg)
be meters/second or unit of speed?
Unit analysis, so sq rt of joule, by definition,
1 joule is equal to 1 newton meter.
Then recall, Newton's 2nd law of motion--the
law of acceleration. Force is mass x acceleration.
Force of newton = mass (kg) x acceleration
meter/sec squared x meter divide by kilogram.
Unit analysis, cancel kilogram, what is left
is m x m--so m/s squared.
Square root is m/s by unit analysis, the unit
of sq KRT is m/s.
This means, if you use a calculator, the speed
of sound at 28 deg cel will be 347.8 m/s.
This means it's about 4 m/s more than the
standard 343. you can also compute for the
standard 343 by substituting it to this formula.
Use the 23 deg celsius.
By now, the distance will be recomputed. Considering
this speed, d=speed x time. Our speed considering
the temp during the experiment, 347.8 m/s
x time.
cancel this.
Therefore distance x 2, will be 695.5.
This is now closer than the
one computed with the standard 343. This is
approx 700m.
This is close to the distance shown in online
map or google map which is 700 m. that's the
reason behind the discrepancy when we did
the computation earlier with the actual distance
because the speed of sound depends on the
temperature.
This time, maybe someone will ask, why is
not the time travelled from the source to
the ear considered? The answer is because
the speed of light is equal to 299,792,458
m/s. But this is speed of light in a vacuum.
Considering it's in the air, divide refractive
index of air which is 1.003 (refractive index
of air) you can find the speed of light in
air which is 299,702,547 ms/. This is the
speed of light in air. In simpler words, approximately
300,000 km/s. This means it's almost instantaneous.
Once the lightning strikes, you will almost
immediately see it. Imagine, 300,000 km/s.
That’s how fast it is. That's the reason
why we did not consider the speed of light
because the speed of light is too fast.
Before I summarize, don't forget to like,
share, comment, and subscribe so you'll stay
updated in the weekly videos I'll upload.
To summarize, when you see the lightning,
start counting 1,000; 2,000; 3,000, that's
the corresponding time the sound approximately
travelled until such time you hear the thunder.
Whichever number you stopped counting at,
multiply it to standard speed of sound which
is 343 m/s. That's the distance between the
lightning location to your ears, approx in
terms of meter. Now I’ll teach you a shortcut.
What if you have big numbers, it’ll be difficult
to multiply mentally. Here's what to do:
The speed of sound 343 m/s is equivalent to
1 second in every 343 meter the soundwave
travels. Convert it to km, there's 1000 m
in every 1 km. Cancel m, therefore when divided,
that's 2.9 sec in every km the sound travels.
To account for error, approx you can 3 secs
per km. For example, let's use this shortcut.
Once you see the lightning start counting.
So time will be 3 secs. Divide the speed reciprocal
of sound which is approx 3 sec per km. Divide
by 3 sec/km. Cancel second, therefore approx
1 km is the distance between you
and the lightning.
That's how simple it is. Just count once you
see the lightning, start counting, then divide
it to 3 that's the distance between you and
the lightning in terms of km. But what if
you see the lightning and hear the thunder
simultaneously? It's possible that you are
very near the lightning location. What if
you only heard it but you didn't get to count
because you passed out? It's possible the
lightning struck you. So stay at home to stay
safe from lightning and Covid.
