Physics · JEE | WAVES

A standing wave on a string of length \( L \) fixed at both ends is represented by \( y(x, t) = 2a \sin(kx) \cos(\omega t) \). The positions of nodes along the string are given by:

1. A
   \( x = (n + \frac{1}{2})\frac{\lambda}{2}, \quad n = 0, 1, 2, 3, \dots \)
2. B
   \( x = \frac{n\lambda}{2}, \quad n = 0, 1, 2, 3, \dots \)
3. C
   \( x = n\lambda, \quad n = 1, 2, 3, \dots \)
4. D
   \( x = (n + \frac{1}{4})\frac{\lambda}{2}, \quad n = 0, 1, 2, \dots \)