The equation of a plane progressive wave is y=0.09 sin8 π(t-(x)/(20)) . When it is reflected at

step 1 In this question we learn about some basic concept of the waves and motion. The question is the

The equation of a plane progressive wave is y=0.09 sin8...

The equation of a plane progressive wave is $y=0.09 \sin 8 \pi\left(t-\frac{x}{20}\right) .$ When it is reflected at rigid support, its amplitude becomes two-third of its previous value. The equation of the reflected wave is (A) $y=-0.09 \sin 8 \pi\left(t-\frac{x}{20}\right)$ (B) $y=-0.06 \sin 8 \pi\left(t-\frac{x}{20}\right)$ (C) $y=0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$ (D) $y=-0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$

The equation of a plane progressive wave is $y=0.09 \sin 8 \pi\left(t-\frac{x}{20}\right) .$ When it is reflected at rigid support, its amplitude becomes two-third of its previous value. The equation of the reflected wave is
(A) $y=-0.09 \sin 8 \pi\left(t-\frac{x}{20}\right)$
(B) $y=-0.06 \sin 8 \pi\left(t-\frac{x}{20}\right)$
(C) $y=0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$
(D) $y=-0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$

Key Concepts

Progressive Wave

A progressive wave is a disturbance that travels through space and time, transmitting energy from one location to another without the permanent displacement of the medium. Its mathematical representation typically includes a time-dependent phase term that describes the movement in space.

Wave Reflection from a Rigid Boundary

When a wave reaches a rigid, fixed boundary, it is reflected back into the medium. This type of reflection is characterized by a phase change, usually a phase reversal, which means that the displacement of the reflected wave is inverted relative to the incident wave.

Phase Reversal

Phase reversal refers to the inversion of the wave's displacement upon reflection at a fixed boundary. This is mathematically represented by a change in the sign of the wave function, which corresponds to a phase shift of ? (or 180 degrees).

Amplitude Modification

The amplitude of a wave can change upon reflection, particularly when energy is not fully conserved between incident and reflected waves due to partial transmission or losses at the boundary. In this context, the amplitude of the reflected wave is specified to be a fraction of the original amplitude.

Direction of Propagation in Wave Equations

The direction of wave travel is encoded in the wave function by the relationship between the spatial and temporal variables. For a wave moving in the positive x-direction, the phase is typically written as (t - x/v), and for a wave moving in the negative x-direction, it is represented as (t + x/v). This change in sign indicates the reversal of the propagation direction upon reflection.

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