Question:medium
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 \( x \) and \( y \) are in meters and \( t \) is in seconds. Which statement(s) is/are correct?
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 \( x \) and \( y \) are in meters and \( t \) is in seconds. Which statement(s) is/are correct?
Show Hint
For wave equations of the form \( y(x,t) = A \cos(\omega t + \phi) \cos(kx) \), remember that the wavelength \( \lambda = \frac{2\pi}{k} \) and the speed of the wave \( v = \frac{\omega}{k} \). Nodes and antinodes are determined by the value of \( kx \).
Updated On: Nov 28, 2025
- A node occurs at \( x = 0.15 \, \text{m} \).
- An antinode occurs at \( x = 0.3 \, \text{m} \).
- The speed of the wave is 4 m/sec.
- The wavelength of the wave is 0.2 m.