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भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन

भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती पर व्याख्यान का आयोजन विज्ञान भारती उदयपुर इकाई एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में कार्यक्रम सम्पन्न उदयपुर, 2 अगस्त। भारतीय रसायन के पिता आचार्य प्रफुल्ल चंद्र रे की जयंती के अवसर पर विज्ञान भारती उदयपुर इकाई (चित्तौड़ प्रांत) एवं बीएन कॉलेज ऑफ फार्मेसी, बीएन विश्वविद्यालय के संयुक्त तत्वावधान में एक विशेष व्याख्यान का आयोजन किया गया। कार्यक्रम का उद्देश्य आचार्य पी.सी. रे के वैज्ञानिक योगदान एवं उनके देशभक्ति से ओतप्रोत जीवन पर प्रकाश डालना था। ज्ञातव्य है कि भारत की पहली फार्मा कंपनी आचार्य रे ने ही बंगाल केमिकल एंड फार्मास्यूटिकल्स लिमिटेड, कोलकाता में 1901 में प्रारंभ की थी। कार्यक्रम में विज्ञान भारती के उद्देश्य एवं गतिविधियों की जानकारी डॉ. अमित गुप्ता द्वारा दी गई। आचार्य पी.सी. रे के जीवन और कार्यों पर मुख्य व्याख्यान डॉ. लोकेश अग्रवाल द्वारा प्रस्तुत किया गया। उन्होंने बताया कि कैसे आचार्य रे ने विज्ञान को समाज की सेवा का माध्यम बनाया और रसायन विज्ञान में भारत को आत्मनिर्भर बनान...
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Phase velocity and Group velocity | Quantum mechanics

Phase velocity and Group velocity

Phase velocity (Wave velocity)

  • If a single monochromatic wave (wave of single frequency or wavelength) travels through a medium, then the velocity through which it propagate is wave velocity.
  • Equation of plane progressive wave propagating in x-direction
            y = a sin (ωt - kx)
  • Here a = amplitude, ω = angular frequency, and k = 2π / λ = wave vector or propagation constant
  • Since in wave motion, the particles of the medium vibrates about their mean position continuously, the velocity acquired by particle during this motion is particle velocity.
  • During this motion, the disturbance (crest or trough) also produced and they also move in the direction in which the wave propagate and also with the same velocity.
  • The velocity of the disturbance through which it advances through the medium is phase velocity (wave velocity).

  • Above equation gives the wave velocity. 
  • Thus the ratio of angular frequency to the propagation constant (wave vector) is known as wave velocity.
  • In equation  y = a sin (ωt - kx), (ωt - kx) is phase of wave motion
  • For the planes of constant phase or wavefronts
            (ωt - kx) = constant
  • Above expression represents the wave velocity.
  • Since the wave velocity is the velocity with which planes of constant phase advance through the medium, and above expression is obtained for such type of wave, so it is also known as phase velocity.
                

Group velocity 

  • In practical life we come across pulse or group of wave of slightly different frequencies. This group of waves are wave packets.
  • A wave packet refers to the case where two or more waves exist simultaneously.
  • The group velocity of a wave packet is the velocity with which the maximum amplitudes of the group advances in the medium.
  • This is the velocity with which the energy in the group is transmitted.
  • The group velocity is defined as the rate of change of angular velocity with respect to wave vector.
            
  • Let a wave packet is made up of two harmonic waves
  • Let on superposition, these waves form a wave packet, then resultant displacement of wave packet
                y = y1 + y2

  • The amplitude of this equation is modulated by

  • Here figure (a) and (b) shows the two waves of slightly different frequencies, and figure (c) shows the resultant wave of these two waves.

  • If △ω and △k are very small. 

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