Superposition Of Waves

Progressive Wave

Properties of Progressive Waves

  1. Each particle executes the same type of vibration.
  2. Particles at the mean position perform SHM.
  3. Have e same amplitude, period, and frequency.
  4. The state of vibration of a particle (phase) changes from one period to another.
  5. V = 0 at extreme position.
  6. The particle attains the maximum velocity after passing through the mean position.
  7. Progressive wave 2 types -

   
   1. Transverse Wave
   2. Longitudinal Wave

Types Of Progressive Waves

  1. Transverse Wave

   > Vibrations of particles are perpendicular to the direction of propagation of the wave. Produces crests and troughs.
   >
   > Can propagate through solids.

  1. Longitudinal Wave

   > Vibrations of particles produce compressions and rarefaction along the wave’s propagation direction.
   >
   > Can propagate through solids and fluids.

Equation of a Progressive Wave travelling along…

  1. Positive x-direction
   y(x,t)=A sin(kx - wt)
   ```
2. Negative x-direction

y(x,t)=A sin(kx + wt)
   ```

Equation of a Simple Harmonic Progressive Wave in different forms

y = A sin(wt - kx)

y = A sin [wt - (2π/λ)x]

y = A sin 2π(nt - x/λ)

y  = A sin 2πn (t - x/v)

y = A sin 2π/λ (vt - x)

y = A sin 2π(t/T - x/λ)

Particle velocity and Wave speed

If the simple harmonic progressive wave is given by

y = A sin (wt - kx)

then,

  1. Particle velocity,
   dy/dt = wA cos (wt - kx)
   ```
2. Wave speed,

v = w/k
   ```

Reflection Of Waves

The phenomenon in which a part of the wave is returned to the original medium with the reduction in its energy and hence in intensity and amplitude is called reflection of waves.

Reflection of a Transverse Waves from…

  1. A denser medium

   
   1. The crest is reflected as a trough
   2. The phase change of 180° or π radians, when transverse waves are reflected from a denser medium

  1. A rarer medium

   
   1. The crest is reflected as the crest and vice-versa with a reduction in amplitude.
   2. No change in phase angle.

Reflection of Longitudinal Waves (Sound Waves) from…

  1. A denser medium

   
   1. To return to normal condition, the particle begins to press in opposite direction, therefore compression gets reflected as compression and vice-versa.
   2. Displacement in reflected is opposite to displacement of the incident wave, therefore phase angle is 180° or π radians.

  1. A rarer medium

   
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