1 Wave Motion

1.1 Characteristics of Wave

  • has Amplitude, \(y_0\) (in meters)
  • has wavelength, \(\lambda\) (in meters)
  • has period, \(T\) (in sec.)
  • has frequency, \(f={1\over{T}}\) (in Hertz or \(sec^{-1}\))
  • has phase, \(\phi\) (in radians or degree)
  • has speed, \(v=f\lambda\) (in meter/sec)
  • has displacement, \(y=y_0 sin(\omega T + \phi)\), \(\omega = {2\pi\over{T}}\)

1.2 Type of wave

  • Longitudinal - peaks and troughs are in same direction of wave.
  • Transverse - peaks and troughs are in perrpendicular direction of wave.

1.3 Relationship with Energy

\(\text{Energry} \propto \text{Intensity} \propto (\text{Amplitude})^2\)

1.4 Energy spread

If there is no friction:

  1. In 3D, the energy spreads on an expanding spherical shell at the speed of the wave. So \(\text{Energy} \propto 1/r^2\). Example, light from sun, or sound from a plane.

  2. In 2D, the energy spreads on an expanding ring. So \(\text{Energy} \propto 1/r\)

  3. In 1D, the energy never dissipates! Example, wave created by snapping a rope.

1.5 Other details

1.5.1 Phase on reflection/transmission

  1. When a wave travels from rarer to denser medium, the phase of reflected wave shifts by 180\(^\circ\).

  2. When a wave travels from denser to rarer medium, the phase of reflected wave remains the same.

  3. The transmitted wave does not undergo any phase shift.

1.5.2 Speed of the wave

Speed of wave depends on property of the medium it is travelling in. It does not depend on frequency, or amplitude.

Speed of sound in metals is more than liquid, which is more than in gas. More dense the medium the faster the speed of sound. (The more rigid/dense, more the speed).

Speed of sound is faster at higher temprature. (The higher the temperature, the faster the molecule can reach other molecule and transfer their energy)

2 Quantum Physics

2.1 Energy of Photon

  • \(\boxed{E = h f\;\;}\) , given by Max Plank, E is energy.

\(f\) is the frequency of photon.

Other relations like: \(\boxed{E = {hc\over{\lambda}}\;\;}\) can be derived using wave property, \(\boxed{c = \lambda f \;\;}\) and for photon \(\boxed{E = cp\;\;}\) p is momentum, E is the energy.

2.2 Duality of Particle and light

When Max Plank said, the light behaves like particle, De-Broglie said, particle may also behave like wave given by:

  • \(\boxed{\lambda = {h\over{p}}\;\; }\) , shows connection beween wavelength (wave property) and momentum (particle property)

2.3 Photo-electric effect

Einstien gave this formula:

  • \(\boxed{\text{(E of photon) = (Work function of Metal) + (K.E. of eletron)}\;\; }\)

It is really conservation of energy equation of the phenomenon, where:

  • Initial state
    • Photon is incident on a metal
  • Final state
    • Photon is completly absorbed
    • It removes electron from the metal with Kinetic Energy
    • Energy needed to make electron free from the metal. This is work function and is property of the metal (some metal hugs electron tighter and so has large work function).

2.4 X-Ray

  • Initial State:
    • Electron accelerated (energy gained = eV, V is voltage between the plates).
    • Electron hits heavy nucleus that has high Z (proton)
  • Final State
    • The nucleus breaks the electron’s speed
    • Sudden breaking releases photon in X-ray region

Interesting Facts

  • X-ray wave-length is $ 1 A . 1 Angstrom = 10^(-10)m $

3 Nuclear Physics

3.1 Decay formula

  • \(\boxed{N = N_0 e^{-\lambda T}\;\;}\)
  • \(\boxed{ln(2) = \lambda T_{\text{half life}}\;\;}\) (learn to derive from above equation)
  • Half life is time taken to for radioactive material to fall to half the original value.
  • \(\boxed{{dN\over{dt}} = -\lambda N\;\;}\) . Rate of decay is proportional to Number of radioactive particles.

3.2 Rays type

  • Alpha ray - is essentially helium with stripped electron
  • Beta ray - is essentially high speed electron or positron
  • gamma Ray - is photon of very low wavelength ( < 0.1 Angstrom)