WAVES......

1. Any by wave equation which is of the form y = f (wt - 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 wt - 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 =w / 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. pth harmonic is produced then the frequency of pth harmonic is
f_p = p / 2l√( T / m ) .
7. If a string is vibrating in nth 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 nth 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 At = 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