Question

A wave disturbance in a medium is described by \[ y(x,t)=0.02\cos\left(50\pi t + \frac{\pi}{2}\right)\cos(10\pi x), \] where \( x,y \) are in meters and \( t \) in seconds. Which statements are correct?

• A. A node occurs at \( x=0.15\,\text{m} \)
• B. An antinode occurs at \( x=0.3\,\text{m} \)
• C. The speed of the wave is \( 4\,\text{m/s} \)
• D. The wavelength of the wave is \( 0.2\,\text{m} \)

Hint:

Standing waves: \begin{itemize} \item Nodes: spatial factor = 0. \item Antinodes: spatial factor = ±1. \item \( v = \omega/k \). \end{itemize}

Answer 1

The Correct Option is A