The equation of a transverse wave is given by
`y=10 sin pi (0.01 x -2t )`
where x and y are in cm and t is in second. Its frequency is

Options

A. `10s^(-1)`
B. `2s^(-1)`
C. `1s^(-1)`
D. `0.01s^(-1)`

Answer

To find the frequency of the transverse wave given by the equation \( y = 10 \sin(\pi (0.01 x - 2t)) \), we can follow these steps:

### Step 1: Identify the angular frequency (\( \omega \))
The general 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.

From the given equation, we can identify that:
\[ \omega = 2 \text{ (the coefficient of } t) \]

### Step 2: Relate angular frequency to frequency
The angular frequency (\( \omega \)) is related to the frequency (\( f \)) by the formula:
\[ \omega = 2\pi f \]

### Step 3: Solve for frequency
Now, we can rearrange the formula to find the frequency:
\[ f = \frac{\omega}{2\pi} \]

Substituting the value of \( \omega \):
\[ f = \frac{2}{2\pi} \]

### Step 4: Simplify the expression
\[ f = \frac{1}{\pi} \]

### Step 5: Calculate the numerical value
Using the approximate value of \( \pi \approx 3.14 \):
\[ f \approx \frac{1}{3.14} \approx 0.318 \text{ Hz} \]

### Final Answer
Thus, the frequency of the wave is approximately \( 0.318 \text{ Hz} \).

---