A travelling wave in a stretched string is described by the equation `y = A sin (kx - omegat)` the maximum particle velocity is

Options

A. `A omega`
B. `omega//k`
C. `d omega//d k`
D. `x//t`

Explanation

To find the maximum particle velocity of a traveling wave described by the equation \( y = A \sin(kx - \omega t) \), we can follow these steps:

### Step 1: Understand the wave equation
The wave equation given is \( y = A \sin(kx - \omega t) \), where:
- \( A \) is the amplitude of the wave,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency,
- \( x \) is the position along the string,
- \( t \) is the time.

### Step 2: Differentiate the wave equation
To find the particle velocity, we need to differentiate the wave function \( y \) with respect to time \( t \). The particle velocity \( v \) is given by:
\[ v = \frac{\partial y}{\partial t} \]

Differentiating \( y \):
\[ v = \frac{\partial}{\partial t} (A \sin(kx - \omega t)) \]
Using the chain rule, we get:
\[ v = A \cos(kx - \omega t) \cdot (-\omega) \]
Thus, the expression for particle velocity becomes:
\[ v = -A \omega \cos(kx - \omega t) \]

### Step 3: Determine the maximum particle velocity
The maximum value of \( \cos(kx - \omega t) \) is 1 (and the minimum is -1). Therefore, the maximum particle velocity \( v_{\text{max}} \) can be found by taking the absolute value:
\[ v_{\text{max}} = A \omega \]

### Final Answer
The maximum particle velocity of the traveling wave is:
\[ \boxed{A \omega} \]

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