Light and Sound Waves

Velocity of Sound Wave
P = psin(w(t-x/v))

I = 2pi2s2v2pn

= Sound = When any object travels faster than sound, it produces noise. e.g. bursting of balloon. The amplitude of sound wave depends on Pressure difference of compression and undisturbed particle.

Longitudinal Waves
When wave changes the medium, the frequency does not change even though its velocity and wavelength changes.

Newton's Formula
v =sqrt[ (Elasticity Modulus of Medium ) / (Density)]  ( E = P )

Laplace's Correction
v = sqrt[ γ x (Elasticity Modulus) / (Density)]     γ = 1.41

Velocity of Sound does not depend on the Pressure of the Medium. Velocity of Sound is directly proportional to the Square root of Absolute Temperature.

v / vo = sqrt { T / To }

v = vo + ( 0.61 ) t   ;   For 1o C rise in temperature, the velocity increases by o.61 times.

Velocity of Sound in Moist Air is greater than its velocity in dry air.

Intensity
I α A2

I α 1/x2, where is the distance from source

Imax/ Imin = (A1+A2)2 / (A1 - A2)2

Measurement of Loudness
Decibel and bel are the unit of Loudness.

Db = 10 log10[I/I0]

where I and I0 are the intensities of sound of hearing and pain respectively.

120 Db = 12 b

= Light = Visible Light lies between 380 and 750 nm wavelength.

Newton's Corpuscular Theory
According to Newton's Corpuscular Theory ;

1) Every source of light emits large number of tiny particles known as 'Corpuscles'.

2) //these corpuscles are perfectly elastic, rigid and weightless.

3) The corpuscles travel in a straight line with very high speeds, which are different in different media.

4) One gets a sensation of light when the corpuscles fall on retina.

5) Different colours of light are due to different sizes of corpuscles.

Could Not explain partial reflection

Huygen's Wave Theory
According to Huygen's Wave Theory ;

1) Light travels in form of longitudinal waves with uniform velocity in homogenous medium.

3) Different Colours of light are due to different wavelengths of corpuscles.

3) When light enters our eyes, we get sensation of vision.

4) A material medium is necessary for propagation . But, light also travels through vaccuum . Hence , there exists a hypothetical medium called as Luminiferous Ether for propagation of light.

Wavefront and Wave Normal
A surface, on which several waves of light reach simultaneously in the same phase is called a '''Wave Surface. A part of the Wave Surface is called as the Wave Normal. Normal Drawn to the tangent of the wave surface, is called as Wave Normal''' The Wave Normal gives the direction of the wave at the wave surface.

Huygen's Principle
Huygen's Principle states that every Wave front acts like a secondary source of light. Thus, light is propagated in all possible directions. The new wavelets are more efficient in the direction of the original wave only. The resultant wavefront at any point is given by tangent to all secondary wavelets at that instant.

Polarisation
The phenomenon of restriction of vibrations of light waves in a particular plane perpendicular to the direction of propagation of wave motion is called as polarisation of light waves.

Brewster's Laws
The tangent of the polarising angle is equal to the refractive index of the refracting medium at which partial reflection occurs.

Polaroid
The property of some doubly refracting crystal absorb the original rays (O-rays) completely and E-rays whose direction is parallel to the optic axis while passing through the crystal, is called dichroism.

Interference
Principle of Superposition : When two or more waves overlap, the resultant displacement at any point and at any instant is equal to the vector sum of instantaneous displacements that would be produced at the point by the individual waves independent of the other.

Young's Experiment
The Interference pattern observed in Young's double slit experiment is hyperbolic. But due to our limitted vision it is observed as straight bands.

Fringe Width or Band Width

X = λD / d = d sinθ

Angular Width

θ = X/D = mλ/d, [where m = n or (2n-1)]

Fringe Width is directly proportional to intensity of light.

If α is the refracting angle, then

d = 2a(n-1)α

For thin transparent sheet placed in one of the waves, shift in fringe is given by :-

S = ( μ-1)t / λ fringes

Biprism Experiment
d = sqrt (d1d2)

X = λD / sqrt(d1d2)

Diffraction
sinθ = λf / a