The equation of a simple harmonic wave is given by `Y = 5sin""pi/2(100t - x)`, where x and y are in metre and time is in second. The time period of the wave (m seconds) will be

Options

A. 0.04
B. 0.01
C. 1
D. 5

Explanation

To find the time period of the wave given by the equation \( Y = 5 \sin\left(\frac{\pi}{2}(100t - x)\right) \), we will follow these steps:

### Step 1: Identify the angular frequency (\( \omega \))
The general form of a simple harmonic wave is given by:
\[ Y = A \sin(\omega t - kx) \]
From the given equation, we can identify:
\[ \omega = \frac{\pi}{2} \times 100 = 50\pi \]

### Step 2: Relate angular frequency to time period
The relationship between angular frequency (\( \omega \)) and time period (\( T \)) is given by:
\[ \omega = \frac{2\pi}{T} \]
Substituting the value of \( \omega \) we found:
\[ 50\pi = \frac{2\pi}{T} \]

### Step 3: Solve for the time period (\( T \))
To find \( T \), we can rearrange the equation:
\[ T = \frac{2\pi}{50\pi} \]
This simplifies to:
\[ T = \frac{2}{50} = \frac{1}{25} \text{ seconds} \]

### Step 4: Convert to milliseconds
Since the question asks for the time period in milliseconds, we convert seconds to milliseconds:
\[ T = \frac{1}{25} \text{ seconds} = 0.04 \text{ seconds} = 40 \text{ milliseconds} \]

### Final Answer
The time period of the wave is \( 40 \) milliseconds.

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