Question

plzz help guys its urgent. no. 47 nd 48
the best ans will be marked brainlist

Answer 1

hey dear here is ur answer
Equation of a plane progressive wave

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

x is  φ = (2π/λ) x

y = a sin (ωt - 2πx/λ)           …... (3)

Since ω = 2πn = 2π (v/λ), the equation is given by,

y = a sin [(2πvt/λ) - (2πx/λ)] 

y =  a sin 2π/λ (vt – x)               …... (4)

Since, ω = 2π/T, the equation (3) can also be written as,

y = a sin 2π (t/T – x/λ)             …... (5)

If the wave travels in opposite direction, the equation becomes,

y = a sin 2π (t/T + x/λ)             …... (6)

hope it helps u dear