The frequency of sinusodial wave y = 0.40cos [2000 t + 0.80] would be
- $1000\, \pi \,Hz$
- $2000 \,Hz$
- $20\, Hz$
- $\frac{1000}{\pi} \,Hz$
The Correct Option is D
Solution and Explanation
To determine the frequency of the sinusoidal wave represented by the equation \( y = 0.40 \cos(2000t + 0.80) \), we need to understand the standard form of a sinusoidal wave.
The general form of a sinusoidal function is:
\( y = A \cos(\omega t + \phi) \)
Here, \( \omega \) is the angular frequency, \( t \) is time, \( \phi \) is the phase angle, and \( A \) is the amplitude.
From the given equation \( y = 0.40 \cos(2000t + 0.80) \), the angular frequency \( \omega \) is 2000.
The frequency \( f \) of the wave is related to the angular frequency by the formula:
\( f = \frac{\omega}{2\pi} \)
Substitute \( \omega = 2000 \) into the equation:
\( f = \frac{2000}{2\pi} = \frac{1000}{\pi} \, \text{Hz} \)
Therefore, the frequency of the wave is \( \frac{1000}{\pi} \, \text{Hz} \).
Conclusion:
The correct answer is \(\frac{1000}{\pi} \, \text{Hz}\).
This is option D. The other options \( 1000\pi \, \text{Hz} \), \( 2000 \, \text{Hz} \), and \( 20 \, \text{Hz} \) do not match the calculated frequency.
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