The equation of a wave id represented as `Y=2sin(Πx - 200Πt)` where x and y are in cm and t is in second. The wave velocity is

Options

A. 100 cm/s
B. 200 cm/s
C. 50 cm/s
D. 400 cm/s

Answer

To find the wave velocity from the given wave equation \( Y = 2 \sin(\pi x - 200\pi t) \), we will follow these steps:

### Step 1: Identify the wave equation format
The standard form of a wave equation is given by:
\[ Y = A \sin(kx - \omega t) \]
where:
- \( A \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency.

### Step 2: Compare the given equation with the standard form
From the given equation \( Y = 2 \sin(\pi x - 200\pi t) \):
- We can identify \( k = \pi \) (coefficient of \( x \))
- We can identify \( \omega = 200\pi \) (coefficient of \( t \))

### Step 3: Calculate the wave velocity
The wave velocity \( v \) is given by the formula:
\[ v = \frac{\omega}{k} \]

Substituting the values of \( \omega \) and \( k \):
\[ v = \frac{200\pi}{\pi} \]

### Step 4: Simplify the expression
The \( \pi \) in the numerator and denominator cancels out:
\[ v = 200 \, \text{cm/s} \]

### Final Answer
Thus, the wave velocity is:
\[ \boxed{200 \, \text{cm/s}} \]

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