Question

deduce an experssion for the velosity of plane progessive wave in a fluid medium mention the assumptions you make

Answer 1

Answer:

An equation can be formed to represent generally the displacement of a vibrating particle in a medium through which a wave passes. Thus each particle of a progressive wave executes simple harmonic motion of the same period and amplitude differing in phase from each other.

Let us assume that a progressive wave travels from the origin O along the positive direction of X axis, from left to right (Fig. 7.6). The displacement of a particle at a given instant is

y = a sin ωt …... (1)

where a is the amplitude of the vibration of the particle and ω = 2πn.

The displacement of the particle P at a distance x from O at a given instant is given by,

y = a sin (ωt - φ) …... (2)

If the two particles are separated by a distance λ, they will differ by a phase of 2π. Therefore, the phase φ of the particle P at a distance