Properties of Transverse waves
1. The particles of the medium vibrate simple harmonically perpendicular to the direction of propagation of the wave.
2. All particles vibrate with the same amplitude, frequency and period.
3. There is gradual phase difference between the successive particles.
4. All the particles vibrating in phase will be at a distance equal ton where n= 1, 2,3,etc. It means the minimum distance between two particles vibrating in phase is equal to one wavelength.
5. Velocity of each particle is the maximum at the mean position and is zero at extreme positions.
6. At any instant, different particles have different displacements.
7. When the particles move above the mean position, it is in the region of crest and when the particles move below the mean position, it is in the region of trough.
8. Due to the repeated periodic motion of the particles, crests and troughs are produced alternatively.
Longitudinal wave motion
The wave in which the particles of the medium vibrate along the direction of propagation of the wave is called the longitudinal wave. A sound wave in air and a wave in a spring which is suddenly compressed and released are examples of longitudinal waves. Longitudinal waves can be set in all media: solids, liquids and gases as they all can sustain compressive stress. When the piston is pushed in, the air near to it is pushed, increasing the pressure at this region. This region pushes in turn to the neighboring region and so on, and a disturbance travels along the tube. On moving the piston back and forth simple harmonically, a series of disturbances pass through the tube, producing a longitudinal wave. In longitudinal wave, the disturbance travels in the form of compressions and rare factions. Compression is the region where particles of the medium come closer to each other, whereas rarefaction is the region where particles are farther apart. So, the density is greater at the compression due to increase in pressure, and it is less at the rarefaction due to decrease in pressure. The distance between two nearest compressions or rare factions is equal to one wavelength.
Propagation of Longitudinal Wave
To understand the propagation of longitudinal waves in a medium, consider nine particles. When the wave travels from left to right, the particles vibrate about their mean positions. After T/8 seconds, the particle 1 goes to the right and completes 1/8 of its vibration. The disturbance reaches to the particle 2. After T/4 seconds, the particle 1 has reached its extreme right position and completes 1/4 of its vibration, The disturbance reaches to the particle 3. The process continues. The wave has reached to particle 9. Here, 1 and 9 are again in the same phase. Here particles 1, 5 and 9 are at their mean positions. The particles 1 and 3 are close to the particle 2. This is the position of condensation. Similarly, particles 9 and 8 are close to the particle 7. This is also the position of compression. On the other hand, particles 4 and 6 are far away from the particle 5. This is the position of rarefaction. Hence, in a longitudinal wave motion, compressions and rare factions are alternately formed.
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