Question

The equation of simple harmonic wave is given as \(y = 5 \sin\frac{\pi}{2}(100t - x)\), where \(x\) and \(y\) are in metre and time in second. The period of the wave is

• A. \(0.02 \, \text{s}\)
• B. \(5 \, \text{s}\)
• C. \(25 \, \text{s}\)
• D. \(0.04 \, \text{s}\)

Hint:

Time period is obtained from angular frequency using \(T = \frac{2\pi}{\omega}\).

Answer 1

The Correct Option is D

Step 1: Comparing with standard wave equation.
The standard form of a wave equation is \[ y = A \sin(\omega t - kx). \]
Step 2: Identifying angular frequency.
From the given equation, \[ \omega = \frac{\pi}{2} \times 100 = 50\pi \, \text{rad s}^{-1}. \]
Step 3: Calculating time period.
\[ T = \frac{2\pi}{\omega} = \frac{2\pi}{50\pi} = 0.04 \, \text{s}. \]
Step 4: Conclusion.
The period of the wave is \(0.04 \, \text{s}\).