Question

The equation of stationary wave along a stretched string is given by

y = 5 sin $\frac{\pi x}{3}cos40\pi t$ , where x and y are in cm and t in second. The

separation between two adjacent nodes is

[CPMT 1990; MP PET 1999; AMU 1999;

DPMT 2004; BHU 2005]

• A. 1.5 cm
• B. 3 cm
• C. 6 cm
• D. 4 cm

Answer 1

The correct option is B

3 cm

On comparing the given equation with standard equation

y = 2 a sin $\frac{2\pi x}{\lambda }cos\frac{2\pi vt}{\lambda }\Rightarrow \frac{2\pi x}{\lambda }=\frac{\pi x}{3}\Rightarrow \lambda =6$

Separation between two adjacent nodes = $\frac{\lambda }{2}=3cm$