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

step 1 Hello students in this question we have equation of progressive wave y equals to 0 .09 sign of 8

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 ( $2 / 3$ )rd 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 ( $2 / 3$ )rd 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) $y=-0.06 \sin 8 \pi\left(t+\frac{x}{20}\right)$

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Key Concepts

Amplitude Reduction Factor

The amplitude reduction factor indicates the change in the magnitude of the wave after reflection or transmission. In a situation where a wave’s amplitude becomes a fraction of its initial value, such as two-thirds, it reflects a loss in energy or influence of the reflection process on the wave's strength.

Reflection of Waves at a Rigid Boundary

When a wave reflects from a rigid boundary, the boundary does not allow any displacement; therefore, the incident wave is inverted upon reflection. This phase change of ?, or sign reversal, is a key aspect of wave behavior at fixed or rigid supports.

Plane Progressive Wave

A plane progressive wave describes a disturbance that moves uniformly in one direction such that its spatial and temporal variations are linked in a linear combination. It is typically represented by a sinusoidal function where the phase (argument) depends on both time and space, indicating the wave's propagation and periodic behavior.

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