A wave is represented by `x=4 cos (8t-(y)/(2))` , wher x and y are in metre and t in second. The frenqency of the wave ` ("in" s^(-1) ) ` is

Options

A. `(4)/(pi) `
B. `(8)/(pi) `
C. `(2)/(pi) `
D. `(pi)/(4) `

Answer

To find the frequency of the wave represented by the equation \( x = 4 \cos(8t - \frac{y}{2}) \), 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, which is:
\[ x = A \cos(\omega t - k y) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

From the given equation \( x = 4 \cos(8t - \frac{y}{2}) \), we can identify that:
- The angular frequency \( \omega = 8 \) (the coefficient of \( t \)).

### Step 2: Relate angular frequency to frequency
The relationship between angular frequency (\( \omega \)) and frequency (\( f \)) is given by:
\[ \omega = 2\pi f \]

### Step 3: Solve for frequency (\( f \))
We can rearrange the equation to solve for frequency:
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{8}{2\pi} \]

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

### Final Answer
Thus, the frequency of the wave is:
\[ f = \frac{4}{\pi} \, \text{s}^{-1} \]

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