Explain the Wave Parameters in details

Phase

Phase defines the position (in terms of distance from mean position) and velocity of a particle oscillating under the influence of a wave. The particles of the medium which are in the same state of motion (at the same displacement from their respective mean positions moving in the same direction) are said to be in phase or differing in phase by 2nπ, where n = 1, 2, 3, …. and the particles of which state of motion are exactly opposite (displacements from the mean position and velocities are exactly opposite) are said to be out of phase or differing in phase by nπ where n = 1, 3, 5, …

  • Oscillations of the particles 1 and 4 are in phase.
  • Oscillations of the particles 1 and 2 are not in phase.
  • Oscillations of the particles 3 and 5 are in phase.
  • Oscillations of the particles 4 and 5 are out of phase.

Wave Speed

Wave speed is the distance travelled by the wave in unit time. In wave motion, the disturbance created at a point of space travels and has a speed. The distance covered per unit time by the wave is known as wave speed.

If we plot the disturbance against position along wave motion at a fixed time, the graph so obtained is called waveform. For a string wave, it is a snapshot of string shape at some moment of time.

The figure shows waveforms at two nearby moments of time t1 and t2. The disturbance (say, peak of string) at P has moved to Q in time t2 – t1. The displacement of wave is \(overrightarrow{PQ}\) in time \(Delta t={{t}_{2}}-{{t}_{1}}.\) Then

v = wave speed \(=frac{PQ}{{{t}_{2}}-{{t}_{1}}}=left( frac{RS}{{{t}_{2}}-{{t}_{1}}} right)\)

We see that waveform of t1 has just translated by PQ, acquiring the new position at t2.

Amplitude

Amplitude a of oscillations of a particle of the medium propagating the wave is the maximum displacement of the particle from its mean position on either side.

Wavelength

Wavelength λ is the distance between two nearest particles (along the direction of propagation of wave) which are in the same phase of vibration. It can also be defined as the distance travelled by the wave in one time period of oscillation.

Wave Frequency

Wave frequency f is the number of times an oscillating particle is at its maximum displacement on one side, during 1 s of motion. It is expressed in Hertz (1 Hz = 1 cycle/s).

Time period

Time period T is the time taken by an oscillating particle to move from mean position to one extreme, then move on to the other extreme position and come back to the mean position. (It is the time the oscillating particle takes to make one complete cycle.) It is the time after which the particle repeats its motion.

Intensity of the wave

Intensity of the wave is the energy transmitted per unit area per second in the form of the wave in the direction of the propagation of the wave by the source. This energy is carried forward by the medium particles which while oscillating transfer the energy to the next particles.

In our further discussion, we assume that as a wave proceeds forward, it does so without any dissipation of energy, i.e., neglecting the effects of air drag, internal resistances, etc. which cause loss of energy as wave progresses. In other words, the amplitude of a simple progressive wave remains same as it progresses forward.

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