A wave is represented by `y=0.4cos(8t-(x)/(2))` where x and y are in metres and t in seconds. The frequency of the wave is

Options

A. `(4)/(pi)s^(-1)`
B. `(8)/(pi)s^(-1)`
C. `(5)/(pi)s^(-1)`
D. `(6)/(pi)s^(-1)`

Explanation

To find the frequency of the wave represented by the equation \( y = 0.4 \cos(8t - \frac{x}{2}) \), we can follow these steps:

### Step 1: Identify the angular frequency (\( \omega \))
The given wave equation can be compared to the standard form of a wave equation:
\[ y = A \cos(\omega t - kx) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

From the given equation, we can identify that:
\[ \omega = 8 \, \text{rad/s} \]

### Step 2: Relate angular frequency to frequency
The relationship between angular frequency (\( \omega \)) and frequency (\( f \)) is given by:
\[ \omega = 2\pi f \]
We can rearrange this equation to solve for frequency:
\[ f = \frac{\omega}{2\pi} \]

### Step 3: Substitute the value of \( \omega \)
Now, substitute the value of \( \omega \) into the frequency formula:
\[ f = \frac{8}{2\pi} \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ f = \frac{8}{2\pi} = \frac{4}{\pi} \]

### Step 5: Calculate the numerical value
Using the approximate value of \( \pi \approx 3.14 \):
\[ f \approx \frac{4}{3.14} \approx 1.27 \, \text{Hz} \]

### Final Answer
Thus, the frequency of the wave is:
\[ f \approx \frac{4}{\pi} \, \text{Hz} \]