Question

The equation of a stationary wave is y = 0.8 cos $\left(\frac{\pi x}{20}\right)sin200\pi t$ , where x is in

cm and t is in sec. The separation between consecutive nodes will be

[MP PET 1994]

• A. 20 cm
• B. 10 cm
• C. 40 cm
• D. 30 cm

Answer 1

The correct option is A

20 cm

On comparing the given equation with

standard equation y = 2 a sin $\frac{2\pi x}{\lambda }cos\frac{2\pi vt}{\lambda }$ ]

We get $\frac{2\pi }{\lambda }=\frac{\pi }{20}\Rightarrow \lambda =40$

Seperation between two consecutive nodes = $\frac{\lambda }{2}=\frac{40}{2}=20$ cm