Understanding Wave Characteristics: Frequency, Wavelength, Energy, and More

in this video we're going to talk about waves and characteristic of waves like frequency wavelength energy amplitude

speed period things like that so let's say if you have a graph and on this

graph you have a sine wave let's say this value is five and this is neg

five and this point is about 10 m so what is the amplitude and the wavelength of this wave if you're given

this information the amplitude of the wave is simply the height between the center and

the peak the peak is called the trough this is known as the

crust so as you can see the amplitude is five another way you can calculate the amplitude is you

can subtract these two numbers and then divide by two so it's the top number minus the bottom number / two so that's

going to be 10 / two and you're going to get five that's another way in which you can calculate the amplitude of a sine

wave now what about the wavelength the wavelength is the length of one

cycle so let me highlight what a cycle is so the wave has to go up then it goes back to the middle and then

it has to make the trip all the way down and then return back to where it started that is one cycle the length of that

cycle is 5 m notice that two cycles is 10 m the second cycle is right here so the wavelength which is typically

represented by the symbol Lambda the wavelength in this example is 5 m let's try another

example so let's say if we have a wave that looks like this and at this

point let's say it's 28 M and the

trough is located at a value of eight and let's say the Crest is located at a value of

-2 what is the amplitude and what is the wavelength what I would do is draw the

center point of the graph notice that it's been shifted up the question is how many units has it

been shifted up the y- AIS to find that value it's simply the

midpoint between the highest value and the lowest value to calculate it we need to take the average of of -2 and 8 the

average is the sum divid two that's going to give us the midpoint -2 + 8 is the same as 8 - 2

which is 6 6 / 2 is 3 so 3 is right between 8 and -2 so we can see what the amplitude is the

amplitude is the distance or the difference between the trough and the midpoint or the center line so 8 minus 3

that's a value of five also you can also calculate it by subtracting 3 minus -2 which is also

value of five or you could use that other equation that I showed you

earlier the amplitude is the difference between the highest point and

the lowest point divided by two so 8 - -2 / 2 8 - -2 is the same as 8 + 2 which is 10 and 10 / 2 is 5 so there's a lot

of different ways in which you can calculate the amplitude of a wave now what about the

wavelength how long is it in this particular example so let's count how many cycles

that we have we need to find the length of one cycle so the

wavelength is basically the distance in meters divided by the number of Cycles our goal is to find the distance

of one cycle so we need to find the ratio between distance and Cycles so this is the first

cycle that's one here's the second cycle that's two here's the third cycle that's

three and we have a half of a cycle so we have a total of 3.5 Cycles so it's 28 /

3.5 let's multiply top and bottom by two so we can get rid of the decimal 28 * 2 is 56 3.5 * 2 is 7 how many times

does 7 go into 56 56 ID 7 is 8 so that's the length of one cycle which is the def as the wavelength so the wavelength is 8

m this position is 16 M and at this point it's 24 and then we have half a cycle which is four which lends us to or

leaves us at uh 28 so now you know how to calculate the wavelength from a

graph so now what about the relationship between frequency and period the period is the time it takes

for the wave to compl complete one cycle so the period is the time divided by the number of

Cycles frequency is the inverse of a period frequency is the number of cycles that the wave makes in a single second

so frequency is the number of Cycles divided by the time the number of Cycles doesn't really

have a unit so for period it's time over Cycles so the unit for period is like seconds the period is the type of time

it's the time it takes to make one cycle so it's measured in seconds frequency is the inverse not the

inverse but the reciprocal of the period so frequency is 1 over P now in some textbooks the period is

represented by capital T so this is the same as 1 over T you probably seen this equation fals 1/ T somewhere so that

just tells the frequency and period or inversely related so the unit for frequency is one over seconds or you can

simply view it as s to Theus one which is the same as the unit Hertz so that's the unit for

frequency so make sure that you know this equation frequency is one over period And if you want to find the

period from a graph use this equation it's the time divided by the number of cycles and if you want to find the

frequency from a graph is the number of Cycles divided by the time consider this

example so let's say instead of having meters on the xaxis we have the unit

time so let's say it's A8 seconds at that point what is the period of this wave so our goal is to find the time it

takes to complete a single cycle we need to find the time it takes to get to that point from the

origin so let's count the number of Cycles so that's the first cycle this is the second

cycle and this this is the third cycle and here's the fourth cycle so there four Cycles the period which I'm

going to use as capital t is the time divided by the number of Cycles so in four Cycles we have a time

of 8 seconds so therefore it's 2 seconds per cycle and that's the period so at this point here

this correlates to two seconds the second cycle ends at 4 seconds the third one ends at six and the last one ends at

eight so the period is two cycles per second now what about the frequency so the frequency is 1 over

period so the frequency is 1 over two which is 0.5 the frequency is the number of

cycles that occurs in a single second so if the frequency is .5 that means that there's .5

Cycles in 1 second now let's make sense of it 1 second occurs here and at this

point we only completed half of a cycle so that's the frequency we've completed half a cycle in 1

second the frequency is the number of Cycles in 1 second so .5 Cycles corresponds to 1 second that's the

frequency so you can say say it's 0.5 Herz let's try another example now let's say if this point

represents. 25 seconds what is the frequency and what is the period so notice that we have the time

it takes to complete one cycle that's the period so therefore the period is25

seconds now to calculate the frequency it's one over the period so 1 /25 gives you four or four Hertz which

is four cycles per second notice that this is 0.5 this is 75 and this is

1 so notice the number of cycles that we complete in one second this is one cycle here's the second

cycle this is the third cycle and this is the fourth cycle so there are four cycles that occurs in a

single second and that's the frequency the number number of cycles that occurs in in one second so that's why the

frequency is four Herz in one second there are four Cycles so you can use the equation to

calculate all of the answers we said the period is the time divided by the number of

Cycles so if you take a time of 1 second and divide it by the four cycles that corresponds to

it you're going to get the period which is 1 over 4 1 over 4 is 0.25 now to calculate the

frequency it's the number of Cycles divided by the time so in this example there are four

cycles that occurs in a single second so four over one gives you a frequency of 4 Hertz so there's many ways in which you

can calculate the period or the frequency if you could find one then you could find the other you just got to

find out which way is easier now let's try one last example with

graphs so let's say if you have a wave that looks like this and at this point you know that the

time is 14 seconds how can you figure out the time at this point which is the time for one

cycle so we know that the period how can you find the period of this particular graph feel free to pause the video and

try this example so notice that we can break this wave into seven

segments 1 2 3 4 5 6 7 so the length of each segment is 14 / 7 so it's 2

seconds so this therefore is 2 4 6 8 10 12 14 and the length of one cycle we could

see is 8 seconds so that's the period so that's a technique that you can use to find the period of a wave if

you're given a value that doesn't end at a complete cycle in such a situation it helps to

break each cycle into four equal parts now let's go over some other equations that you need to

know you need to know the relationship between wavelength and frequency as the wavelength increases which is

represented by this Lambda symbol the frequency which is V or you can write F if you want the frequency decreases the

wavelength and the frequency are inversely related now we know that the

frequency is inversely related to the period so as the wavelength goes up up the period goes

up the wavelength is inversely related to the energy as the wavelength goes up the energy goes

down so wavelength and period are directly related and the

frequency and the energy are directly related the equation that relates wavelength and frequency is this one C

is equal to Lambda * V or we'll just use Lambda time f f is fre C is the speed of light this is how fast

light travels in a vacuum or empty space so the speed of light is 3 * 10 8 m/s and that's very fast that means in 1

second a light can travel a distance of 300 million met now let's say if you have a

wavelength of 600 nanometers how can you use this information to calculate the frequency

of this wavelength frequency is the speed of light /

wavelength so it's going to be 3 * 10 8 m/s divided by we don't want to put 600 nanometers because nanometers and meters

they don't match we need to convert the nanometers into meters it turns out that one nanom

is equal 1 * 10- 9 M so 600 NM is simply 600 * 109 M so we can see that the unit meters will cancel

and you're going to get the unit 1 / s one/ seconds which is frequency which is the same as

Hertz so let's type it in 3 * 10 8 / 600 * 109 gives you a frequency of 5 time 10^

14 Hertz now once you have the frequency of a photon of light you can calculate the

energy of that Photon using this equation the energy is equal to Plank's constant time

frequency Plank's constant is 6626 * 10-34 Jew time

seconds so let's pay attention to the units frequency which is in hertz we can also represent

it as one/ seconds so notice that the unit seconds cancel which means that in this equation

the energy of the photon is in Jews so if we multiply those two numbers this is going to give us an energy value

of 3313 * 1019 now sometimes you may need to

convert it to electron volts one electron volt is equal to 1.62 *

1019 so to convert it we need to divide by 1.62 * 1019 as you can see the unit Jewels will

cancel if we set it up this way notice that the 10^9 value will cancel as well so all we need to do is

type in 3313 / 1. 1602 and that's going to give us the energy and electron volts so it's

going to be 2.07 electron volts so far we've considered how to calculate

the frequency of a photon in pure empty space in a vacuum and also the energy under those

conditions but let's say if light is passing through water or glass or Diamond what's going to

change whenever light passes through a material it slows down the speed changes and also the wavelength Chang changes

with it but not the frequency the frequency Remains the Same there's an equation that helps you

to calculate the speed of light in a different material here's the equation V not the

frequency V but velocity V is the speed of light in a vacuum divided by the index of

refraction so C is still 3 * 10 8 this is the speed of light in a vacuum n is the index of a fraction

so let's use water as our example the index of refraction for water is about 1.33 now V represents the speed of light

in this material in this case the speed of light in water we can use this equation to calculate the speed of light

in glass or the speed of light in Diamond as the index of a fraction increases the speed of light in that

material decreases the index of refraction for glass is about 1.5 for Diamond I believe

it's about 2.4 so light travels much slower in Diamond than it does in glass and light

travels slower in glass than it does in water but in pure empty space light travels at its maximum speed of 3 * 10

8 m/s so let's let's calculate the speed in water so all you have to do is divide

3 by 1.33 and you should get

2. 26 and then you can simply add this value time 10 to 8 m/s so as you can see light is a little

bit slower in water than it is in pure empty space now what about the wavelength

we see that as the index of refraction decreases the speed of light decreases but what about the wavelength

what effect does it have on it as the index of refraction increases it turns out that the wavelength decreases as

well the equation that you need is the wavelength in a material with an index of

refraction of n is equal to the wavelength in empty space / n so this time let's choose the same

wavelength that we had in the last example that is 600 nanom so it's going to be 600

nanom divided by the index of a fraction for water which is 1.33 and so we're going to get a

wavelength of approximately 41.1

nanom so that's the wavelength of light in water so as you can see the wavelength in empty space

was originally 600 but now in water it decreased to 451 .1 and the

speed is now 2.26 * 10 8 so what we're going to do is calculate the

frequency so using this equation we know that the speed of light is the wavelength times

frequency now we have to use not the speed of light of or in a vacuum we have to use the speed of light in water which

is V and we have to use the wavelength in water which is Lambda n times frequency so the frequency is going to

be V divided Lambda so the speed of light in water is 2.26 * 10 8 m/ Second and the wavelength

of light in water in this example is 41.1 * 109 M so if we divide those two numbers

we're going to get 5.01 * 10 14 Hertz now granted these answers are

rounded so that's where the 01 comes from but if we didn't round it we would get exactly 5 * 10^ 14 Herz which is

what we had in a previous example so notice that the frequency it does change if light is in empty space or if it's in

water so as light passes from one material to another the speed of light will change

and the wavelength will change but the frequency Remains the Same and because the frequency is the same the energy is

going to be the same as well because the energy is proportional to the frequency so we're going to get the same

answer as we did in the last example so here's a question for you let's say if you have two

materials let's say this is diamond and this is glass as light passes through

Diamond to Glass what's going to happen to the speed of light will it increase or

decrease as it travels from Diamond to Glass think about it now we know what happens as light

travels from empty space to water so let's say if we have a container with water as light travels from air to water

it's going to bend this is known as refraction and as it passes from air to

water will the speed increase or decrease so you have to think about what's happening um to the index of

refraction or how it's changing the index of refraction of air is one and for water is

1.33 so the index of refraction increases in this particular example as the index of refraction

increases the speed of light decreases light travels slower in water than it does in air because water has a

higher index of refraction and also the wavelength will decrease as it goes from Air to water the frequency is going to

stay the same and the energy of the photon will be the same as well now from Diamond to Glass the

reverse is true the diamond has an index of refraction of 2.4 and for glasses 1.5 so we're going from a material that

has a high index of refraction to a material that has a low index of refraction therefore n is decreasing and

whenever the index of refraction decreases the speed of light will increase and the wavelength will

increase as well as light travels from Diamond to Glass now the next thing that you need

to be familiar with is the electromagnetic spectrum we're going to rank it

from Long wavelength to short wavelength or from low energy to high energy so the first one in the list are

radio waves radio waves have the lowest energy the lowest frequency but the longest wavelengths after radio waves

you have microwaves and then after microwaves there are there's infrared and then

after that you have visible light voy Biv red

orange yellow green blue there's Indigo and then

there's Violet after Violet you have ultraviolet radiation

and then xrays and then uh gamma rays and after that you have a cosmic radiation which

I'll just write C for Cosmic radiation so as you go to the right in the electromagnetic

spectrum the frequency increases so gamma radiation has a higher frequency than X-rays and also

the energy increases frequency and energy are directly related so x-rays has a lot more energy than UV

rays now on the left the wavelength increases radio waves they have the lowest energy but they have the longest

wavelength so which one has a higher frequency microwaves or ultraviolet light so frequency increases to the

right ultraviolet light has a higher frequency now which one has more energy blue light or red

light energy increases to the right so since blue is to the right of red blue has more energy now which one has a

longer wavelength xrays or gamma rays wavelength increases to the left so xrays which is to the left of gamma rays

x-rays have a longer wavelength now which one has a lower frequency infrared radiation or red

light IF frequency increases to the right the one to the left has the lower frequency so that's infrared

radiation now which one has less energy microwaves or green light so energy decreases to the left so

microwaves have less energy than green light and which one has a shorter wavelength infrared or ultraviolet

radiation the shorter wavelength is the one that's on the right side so ultraviolet radiation has the shorter

wavelength now the next thing you need to know is the range of the visible light

spectrum red light is around 700 NM in wavelength and violet light is about 400 NM

so at this point it's 700 nomers and over here it's 400 violet light is about between 400

and 450 blue light it ranges about 450 to 500 and green light is 500 to 570

Nom yellow light has a smaller range it's like 570 to 590 orange is about 590 to

620 and red light has the the longest range it's 620 to 700 so now you know the visible light

spectrum and the wav lamps that corresponds to each color so that is it for this video thanks for watching and

have a great day