Superposition Of Waves
Progressive Wave
Properties of Progressive Waves
Each particle executes the same type of vibration.
Particles at the mean position perform SHM.
Have e same amplitude, period, and frequency.
The state of vibration of a particle (phase) changes from one period to another.
V = 0 at extreme position.
The particle attains the maximum velocity after passing through the mean position.
Progressive wave 2 types -
- Transverse Wave
- Longitudinal Wave
Types Of Progressive Waves
- Transverse Wave
Vibrations of particles are perpendicular to the direction of propagation of the wave. Produces crests and troughs.
Can propagate through solids.
- 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…
- Positive x-direction
y(x,t)=A sin(kx - wt)
- 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,
- Particle velocity,
dy/dt = wA cos (wt - kx)
- 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…
A denser medium
- The crest is reflected as a trough
- The phase change of 180° or π radians, when transverse waves are reflected from a denser medium
A rarer medium
- The crest is reflected as the crest and vice-versa with a reduction in amplitude.
- No change in phase angle.
Reflection of Longitudinal Waves (Sound Waves) from…
A denser medium
- To return to normal condition, the particle begins to press in opposite direction, therefore compression gets reflected as compression and vice-versa.
- Displacement in reflected is opposite to displacement of the incident wave, therefore phase angle is 180° or π radians.
A rarer medium
- \