For a string clamped at both its ends, which of the following wave equation is lare valid for a stationary wave set up in It? (Origin is at one end of string)

Options

A. `y=Asin kx.sin omegat`
B. `y=A coskxsinomegat`
C. `y=Asinkx.cos omegat`
D. `y=A cos kxcos omegat`

Explanation

To determine the valid wave equation for a stationary wave set up in a string clamped at both ends, we need to analyze the characteristics of stationary waves and the boundary conditions imposed by the clamping of the string.

### Step-by-Step Solution:

1. **Understanding Stationary Waves**:
A stationary wave is formed by the superposition of two waves traveling in opposite directions. The general form of a stationary wave can be expressed as:
\[
y(x, t) = A \sin(kx) \cos(\omega t) \quad \text{or} \quad y(x, t) = A \cos(kx) \sin(\omega t)
...