Question

The equation of a stationary wave along a stretched string is \[ y = 5\sin\left(\frac{\pi x}{3}\right)\cos(40\pi t), \] where \( x,y \) are in cm and \( t \) in seconds. The separation between two adjacent nodes is

• A. 1.5 cm
• B. 3 cm
• C. 6 cm
• D. 14 cm

Hint:

Standing waves: \begin{itemize} \item Node spacing = \( \lambda/2 \). \end{itemize}

Answer 1

The Correct Option is B

Concept: Nodes occur when spatial sine term = 0. Step 1: {\color{red}Condition.} \[ \sin\left(\frac{\pi x}{3}\right) = 0 \] \[ \frac{\pi x}{3} = n\pi \Rightarrow x = 3n \] Step 2: {\color{red}Node spacing.} Adjacent nodes: \[ x_{n+1} - x_n = 3\text{ cm} \]