in this video we will talk about the sinusoidal waves in their importance in physics we will discuss the very general equation of these periodic waves and the different parameters used in these waves we will discuss those parameters in their relation to the physical quantities so the questions that we will answer in this video or the very first one that what are sinusoidal waves what is the amplitude and is it related to the intensity of a wave then what is wavelength in which property it is associated with for we will discuss that whether the energy of a wave is changed when we change the intensity of a wave and then what's the difference between the frequency and special frequency this frequency we call the time frequency and special frequency is the frequency depending on space then we will talk about the photo electric effect the reason that why electrons were not ejecting out of the metal surface when we were increasing the intensity and we will discuss that why FTIR spectra are plotted in wave numbers on the x axis what is the phase shift and which property emerges out when we discuss different waves are the same waves with a phase shift in them and finally we will discuss the case space that whether it is a momentum space or it is a reciprocal space that we study and solid-state physics so the very first there are many definitions of a wave a wave is actually a disturbance in a medium that carries energy alternate moment of particles we can also define it is a wave is a disturbance of one or more fields said they'd the field values oscillate repeatedly about a stable equilibrium reading this is a wave equation in which we see that the function I am representing it with a sign it can be represented with any function such that that function is dependent on space in time then the double derivative with respect to time of the attraction is equal to the double derivative of that function with respect to space provided with a constant of proportionality is v square and this V becomes equal to C the speed of light when we come to electromagnetic waves the solution of this equation is sine a function of X T a sine KX plus minus Omega T plus Phi the solution can also be written is a cos means sine is replaced with cos and both are actually sinusoidally varying periodic functions you know the only difference between sine and cos is actually there PI by 2 radiant phase-shift so let's discuss this relation here a is actually the amplitude and K is the wave number which is related to the wavelength by 2 pi by lambda lambda being the wavelength of the wave Omega is the angular frequency which is related to the linear frequency by 2 pi nu nu being the frequency of the wave while Phi is the phase of the wave so all information is included in this equation which we will discuss one by one the very conceptual thing that we will have to keep in mind that all the motions depicted here are actually the simple harmonic motions if I consider a particle moving in a circle then it is equivalent to a particle moving like a sine wave or a particle going up and down means at h-2a spring are it's going in a pendulum the equation of them is the same which is the simple harmonic motion equation so these are these motions this these are actually the different representations of the motion while they are the same motions if I look here to the circle then the particle completes one complete cycle in true pi radians are 360 degrees similarly here the particle completes one cycle in 360 degrees are two pi radians similarly here we can see here the green dot here that the green dot is represented on a circle here when it reaches the maximum amplitude half of the circle is covered in when it is big then the very next hop is covered similarly the pendulum motion is also the same thing so discussing the very first thing which we call the amplitude of a wave amplitude of a wave is actually its maximum height from the straight line which we have behaving the x axis so the height of the crest of it we call the amplitude of the wave if I consider three waves the same waves are here the only difference between them is their amplitude like this wave is Haiming mV should equal to one the green is naming amplitude equal to two while the red one is having four times more amplitude compared to the place so we are having these waves is a different amplitude having different amplitudes now the big question here is what happens when two are more than two waves same waves but having different amplitudes then which property of the wave is affected okay the question is about which property of a wave is different when two waves are more than two waves have different amplitudes is it energy intensity wavelength and wave number so the answer is intensity because intensity is really proportional to the square of the amplitude more the amplitude of a wave more will be the intensity of the wave now we will have to understand the intensity of it more intensity is proportional to the power of the source and inversely proportional to its unit area some intensity is not only related to the power it is also related to the distance from the power we know that power is energy per unit time while intensity is power per unit perpendicular area this implies that intensity is equal to energy per unit perpendicular area per unit time so intensity of a wave not only depends on the energy but also on the cross sectional area and the time as well so if the amplitude is doubled the intensity is squad report because intensity is proportional to the square of the amplitude now we can see that if I write electric field then this is e naught cos Omega T where II not is the amplitude of the electric field in Omega is the variation or the frequency of this electric field and the intensity of this electric field will be equal to let me write the electric field the electric field is written is equal anat cos Omega T where a naught is the amplitude of the electric field in omega is the variation or the angular frequency of this electric field so its intensity will be equal this intensity will be proportional to e naught squared because e naught is the amplitude and this is the constant of proportionality similarly in magnetic field V naught cos Omega T we will have the intensity equal to V naught square and then constant of proportionality which is C over 2 mu naught here epsilon naught is the permittivity of free space in C is the speed of light this is the permeability of free space and see again the same speed of light so let us understand the relation of intensity with unit area that we are having this relation that intensity is the power per unit perpendicular area if this is a source in the source power is equal to P and the sphere area is 4 PI R square so if I consider this segment only then from this segment four five is actually the solid angle means the angle which is made by considering this page this is all the solid angle now if I'm our distance away then this much area the light or the car is passing through this much area which is a and this is equal to R now when I go to times R then what will happen that intensity will come by intensity will get down four times because this R I replace with two R then it will become one word for an R square so the intensity will come down by four times let's say this is the unit area this is this unit area then this unit area is actually becoming four times is we go to are away from here because the solid angle will be kept the same when we go three R then one over three are become nine R square so intensity will go one over nine times of the present intensity so is we go then the intensity is getting down is a square of the radial distance from date source point now the question is when the intensity of a wave is change does it change its energy the straightforward answer is yes but we are having another answer which is eight four and it says that yes under certain certain restrictions and this may seems to be the most suitable answer because intensity is not only depending on energy but also on the perpendicular area is will is time so the most suitable answer is the fourth and let me explain this thing by explaining the photoelectric effect now in photoelectric effect we know that when we shine a light of certain energy on a metal surface then the electrons on the surface the metal surface electrons absorb that energy if the energy of the photon is more equal or more than the surface binding energy of this electron then this electron will be ejected out of the metal surface now in photoelectric effect we know that if the energy will be of the verb will be less than the energy of the threshold energy or the energy the surface binding energy of these electrons then by increasing the number of energy sources the electrons are not being ejected out we increase more the intensity of the electrons are not ejecting out so here we see that intensity of a wave is not changing energy this is not rather true because in photoelectric effect something else is happening and we will discuss this situation as well in the coming slide but I can say that intensity is actually the number of photons when this was one light then few photons were emitted let's say for example one light hundred photons were emitted then with the help of six sources we will have 600 photons so the total energy has increased but the individual energy of a photon will remain the same if single burb is emitting 10 electron volt for norm then increasing the number of birds will increase the number of photons which we say that increase the number increase the energy of the total energy of the photons but the individual energy of the photon will remain the same if we change the source and let's say this is not a source which is having the photons which it emits they are having the energy more than the threshold energy of these electrons then what will happen that the electrons will be ejected out of the metal surface Einstein actually resolved this issue by saying that one photon will interact with one electron only so when we increase the source energy then when we change the source such that the source is no emitting photons in each photon is himming its energy more than the surface binding energy are the work function of these electrons then they will be ejected out now in this situation if we increase the number of sources then what we are doing we will increase the number of photons in this increase in number of photon will cause more electrons to get out of the metal surface serve not here the individual energy of the photon has been changed by changing the source so we see that when intensity is increased although the total energy is increased because the total energy is the sum of the energy of all photons hi