hello everyone this number 12 is about
why we'll be talking about the nature of
light and solving equations that relate
wavelength to frequency also we'll talk
about sound and the equations that
relate the speed of sound to the
temperature now with regard to the light
we see that light has dual nature and
your nature means that it has both wave
properties as well as particle
properties let's talk about the property
first the wave nature of light right
right other waves whether its water wave
sound waves mechanical waves and so on
they have wavelength frequency velocity
they undergo certain properties like
refraction diffraction interference
dispersion and so on
we'll talk about each one of those in
this lesson now we try to focus on
solving problems that involve the wave
nature of light suppose you turn on your
radio and you told this to 104 megahertz
FM dial what is the wavelength coming
from those fascinating towers and so if
we analyze the problem we are given the
frequency which is 104 mega he'll and if
you recall mega represents 1 million
which is 10 to the 4 6 and also we know
that the speed of all electromagnetic
waves is 3 times 10 to the 4 8 meter per
second and radio waves are part of the
electromagnetic spectrum so it will have
the same speed as all the necromantic
waves 3 times 10 to the 4 8 meter per
second so given this information the
frequency and the velocity of the wave
we can use the equation the speed of
light or the speed of anyways be equal
to the frequency time to advance this is
the equation we have used now here we
are given the frequency and we are give
the speed we know the speed so we need
to rearrange the equation to solve for
the wavelength and we have to make sure
that we write the frequency in Hertz and
because health is one over second and
when you divide the speed of the wave
which is meter over second by the
frequency in Hertz which is one over
second one over second in the numerator
will cancel out with one over second in
the denominator and we'll get answer in
meters so that's why we have to convert
and frequency from whatever unit you are
given to her here we are given the
frequency in megahertz to convert it to
her we have to multiply by 1 million
because mega is 1 million which is in
turn four six this of course will give
you one of those four million half and
if you want to write it in the flower of
the notation in the sub segment ation we
have to have one non-zero digit to the
left of the decimal point so if you move
this one point two places to the left
you have to add 2 to the 6 and this will
give you one point zero four times 10 to
the power 8 if you don't want to go does
it to power up imitation that's your
choice as well you can just divide by
104 million which is 104 and decided six
zeros but when you carry out the cut
reason you should get two point eight
meters and let me remind you here with
hard to do calculations that involve
power of 10 and to do calculations that
involve power of Sanitation you have to
use the EE or exp press
so we'll go 3 and then we press 2nd
comma this will give you the AE and this
written has a small lowercase e then 8
so this means three times simple for a
recall that the EE press replaces times
1 0 which is 10 raised to the power so
you are replacing four presses by one
press and you can go back to our
exercises over calculators that we did
in the first week of the class divided
by one point zero four times into the
power 8 so we go one point zero four and
hit the EE
so that's
times then to the power and now we like
to eat and we'll press ENTER and as you
see the answers it got to be two point
eight eight meters to be exact so this
should be two point eight eight meters
okay so go ahead and try to solve
question number one in discussion
exercises number twelve
notice here that you are given the
frequency of an AM dial and again AM is
a radio wave so it has the speed of the
light which is three times ten to the
power 8 meter per second and you are
given the frequency in kilo Hertz so
again you have to convert it to her so
you'll be dividing the speed of light by
eighty three thousand Hertz and this
will yield the wavelength and again here
let me show you the capitation you take
three times ten to four eight so 3e8
that means time since the 48 divided by
eight fifty kilohertz which is 83
thousand Hertz or we can write as eight
point three times ten to the power 4
because 83,000 when you move the decimal
point to the left four places it will
give you eight point three and you have
to multiply by 10 to the power 4 because
you moved it for this is the next and
this should be at around three thousand
six hundred 14 meters okay a second
video will talk about the nature of
light and they sort of sound here in
this video will focus on solving
problems using the equation of wave
which is the speed of anyway be equal to
the frequency times the wavelength and
also using the equation that enable us
to find the speed of sound sound depends
on the temperature of the medium because
sound moves through compressions and
refraction of the medium
unlike light that propagates through the
vibration of the electric and magnetic
field and hence does not need the medium
to carry the light that's why I can move
through back
found on the other hand requires medium
and the temperature of the medium will
determine a speed because the higher the
temperature the higher the thermal
kinetic energy of the particles of the
medium and when the thermal kinetic
energy is high sound will move faster in
a high thermal kinetic energy medium it
was found that the speed of sound at
zero degrees Celsius is equivalent to C
hundred thirty one meter per second
which is around one thousand 287 foot
per second or 740 miles per hour
recall that the speed of light is
186,000 miles per second so light is
much faster than sound and that's why we
see lightning before we hear the Thunder
Coast lightning and thunder have happen
at the same time but we see it before we
hear it this is the equation of speed of
sound as a function of the temperature
at zero degrees Celsius is speed is 331
meter per second with each degree
Celsius you have to add point six one
and this is meter per second of Celsius
notice here that Celsius would cancel
out T here is the temperature and it's
in Celsius as soon as will be meter per
second so don't flip the units confuse
you meter the second would be the answer
to the calculation of this equation so
for example let's assume that you have a
tuning fork that has frequency equal to
250 Hertz and suppose you set it to
vibrate and the temperature of the room
was 20 degrees Celsius what would be the
speed of the sound
propagating from this vibrating tuning
fork do you do that we have to apply the
equation and when you do that mixing you
must apply the temperature for us by the
cost of four six one then add 331 so you
multiply point six one by 20 degrees and
F 3 31 and this will give you three
hundred forty three point two meter per
second so we got the speed here the
question is what is the wavelength to
find out that we have to use the John
Christian or speed of tweed which is the
speed of any weight is equal to the
frequency times the wavelength and many
arranges to fall for the rhythm so the
wavelength will be the velocity of the
wave divided by the frequency now the
blocks of the rate here is three hundred
forty three point two meter per second
we divided by the frequency which is 250
Hertz and this will yield 1.37 meters
okay stand of the solve similar problem
here determine the wavelength of sound
propagating from a 440 of tuning fork
vibrating in a 25 degree celsius air now
to find the wavelength we have to find
the speed of the wave and here the wave
is sound
hence we cannot use the speed of light
which is three times ten to the
photogate meter per second so what
equation should we use given the
frequency which is 440 well and the room
T which is 25 degrees Celsius now we
know not to find the way the wavelength
we have to divide the speed of the wave
by the frequency now what will be the
speed of the wave here now one common
mistake is the students using the speed
of light which is three times 10 to the
power 8 meter per second this is a big
error because the question is about
sound tuning fork will produce sound
waves not electromagnetic waves so we
can't use the three constants for heat
instead in order to find the speed of
the sound we have to use a question that
we just learn the speed of any sound is
equal three thirty one meter per second
plus point six one potential ago so
basically with beam applying point six
one by 25 degrees Celsius and then
adding three thirty one and the three
thirty one is the meter per second now
if you can advocate reason this should
give you a c4 p 6 meter per second so
that's the speed of the sound now this
is not the answer yet we are asked to
find the wave map so to find the
wavelength we can go back to our
equation here
and plug the values of the speed that we
got and divide by the frequency so the
wave rail will be 346 meter per second
divided by the frequency which is 440
huh
and the number house is one over second
so one over second here will cancel out
with one over second and we'll get the
answer in meters which will come out to
be around point seven eight six meters
okay let's look at more questions here
in the discussion question to receive
you are given a frequency of the sound
wave to be two thousand third and you're
asked to find the distance between
crests or compressions of the wave of
course in the case of sound waves sound
waves are longitudinal waves it
propagates by means of compression and
refraction so it's basically a distance
for example between two successive
compression which cause you deliver so
we are asked to find the Wigner and here
it asks you to take this video sound to
be 344 meter per second so we don't mean
exactly the speed of sound using the
temperature sense is already given to us
so to find the wavelength will divide
the speed of the song give it the switch
is 344 meter per second by the frequency
which is 2,000 Hertz and this will be a
point one seven two meters okay question
number four again try to solve it
yourself first and whenever you're done
you can seek the solution and here we
are asked to find the wavelength of an
x-ray that has frequency of one times 10
to the power 18 house now x-ray is part
of the electromagnetic spectrum hence it
has the speed of light which is three
times 10 to the power 8 meter per second
so to find the wavelength we divide the
speed of light by the frequency given
and this will leave three times 10 to
the negative 10 meters and we expect the
wavelength to be very thought because x3
has very high frequency in the next
video we'll talk about the nature of Y
in more details we've got more than
the sound waves using the Invisibles
briefly and also will solve more
homework problems and those homework
problems will address several properties
of life like reflection refraction
diffraction interference and dispersion
thanks for watching
