1. Any  by wave equation which is of the form y = f (t - kx ) represents a    
    progressive  wave :
  a. If the sign of t and x are opposite, wave is propagating along positive x-axis.
  b. If the sign of t and x is same , wave is propagating along negative x-axis
  c. If t - kx = phase = constant, then  the shape of the wave remains constant.
  d. For a given t, y-x graph gives the shaoe of pulse or string.
  e. Wave speed ,  c = / k.
   f. Particle velocity, v = slope = y / t.
2. Total energy of a loop remains constant.
3. The particle of medium at node remains permanently at rest. Also nodes              divide the medium into loops.All particles of a medium  lying in a loop  vibrate     in the same phase having different amplitude.
4. At node displacement is zero but pressure is maximum and at antinode              displacement is maximum but pressure is minimum.
5. For a given t,the y-x graph gives the shape of the string.
6. If the strings vibrates in 'p' loops. p^th harmonic is produced then the frequency     of p^th harmonic is
        f_p = p / 2l ( T / m ) .
7. If a string is vibrating in n^th mode of vibration,then
    a.number of harmonics =  n
    b. number of loops = n
    c. number of nodes = n+1
    d. number of antinodes = n
    e. number of overtones = n -1
8. The meaning of octave is 2, eg- if f₂ is n^th octave higher than f₁ , then
     f₂  = 2ⁿ f₁
9. The amplitude of the reflected wave is [ (c₂ - c₁ ) / (c₁ + c₂ ) ]A_i and the 
     amplitude of transmitted wave is  A_t = A_i [ 2c₂ / (c₁ + c₂ )].
      A_i = amplitude of incident wave in first medium
      c₁ = speed of wave in first medium
      c₂ = speed of wave in second medium
10. Melde's law : p T = constant