The frequency of the sinusoidal wave
`y=0.40 cos [2000 t +0.80 x]` would be

Options

A. 1000 Hz
B. 2000 Hz
C. 20 Hz
D. 1000 / `pi` Hz

Explanation

To find the frequency of the sinusoidal wave given by the equation \( y = 0.40 \cos(2000t + 0.80x) \), we can follow these steps:

### Step 1: Identify the angular frequency (ω)
The general form of a sinusoidal wave is given by:
\[ y = A \cos(\omega t + kx + \phi) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number,
- \( \phi \) is the phase constant.

From the given equation \( y = 0.40 \cos(2000t + 0.80x) \), we can see that:
\[ \omega = 2000 \, \text{rad/s} \]

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

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

Substituting the value of \( \omega \):
\[ f = \frac{2000}{2\pi} \]
\[ f = \frac{1000}{\pi} \, \text{Hz} \]

### Step 4: Conclusion
Thus, the frequency of the sinusoidal wave is:
\[ f = \frac{1000}{\pi} \, \text{Hz} \]

### Final Answer
The frequency of the sinusoidal wave is \( \frac{1000}{\pi} \) Hz.

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