The particles of the medium vibrate simple harmonically along the direction of propagation of the wave. All particles have same amplitude, frequency and period. There is a gradual change in phase between the successive particles. The velocity of each particle is the maximum at its mean position and zero at extreme points. When the particles move in the same direction as the propagation of the wave, it is in the region of compression
But when they move in the opposite direction to the direction of propagation of the wave, it is in the region of rarefaction.
When the particle is at the mean position, it is either a region of maximum compression or rarefaction.
7. Due to repeated periodic motion of the particles, compressions and rare factions are produced alternately. These compressions and rare factions travel forward in the medium with the velocity equal to that of the wave.
Comparison between Transverse and Longitudinal Waves.
Transverse Waves
1. The particles of the medium vibrate perpendicular to the direction in which the wave advances.
2. It travels, producing crests and though in medium.
3. It can propagate only in solids and at the surface of liquids.
4. There is no pressure variation.
5. Particle displacement is perpendicular to the direction of wave propagation.
Longitudinal Waves
1. The particles of the medium vibrate in the same direction in which the wave advances.
2. It travels, producing a series of compressions and rare factions in the medium.
3. It can propagate in all type of media: solid, liquid, gas.
4. The pressure and density are the maximum at compression and minimum at rare factions.
5. Particle displacement is parallel to the direction of wave propagation.
Progressive Wave
A wave that travels from one region of medium to another is called the progressive wave. In such wave, the disturbance travels forward and is handed to the next particle after a certain time. So, all particles vibrate with the same amplitude and frequency, but the vibration begins a little later than the particle immediately before it. No particle is permanently at rest, but they vibrate with different phase. A progressive wave may be a transverse or longitudinal wave.
Equation of a progressive wave
Suppose a wave traveling from left to right along x-axis. Consider a particle at the origin O vibrating simple harmonically and its displacement at any instant t is being given by y= a sin.
Where A is the amplitude of the particle and w, its angular velocity. Now let us consider another particle P at a distance x from O. Since the disturbance will reach later to the particles to the right of O, the phase of motion of these particles lags to that of O, and it goes on increasing.
Principal of Superposition.
Two or more progressive waves can travel simultaneously in a medium without affecting the motion of one another. When they reach at a point, the resultant displacement of the particle at that point is equal to the vector sum of the displacements produced by each wave separately. This is obtained according to the principle of superposition, which can be stated as:
When two or more waves are passing through a medium at the same time, the resultant displacement at any point is equal to the vector sum of their individual displacements at that point.
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