Question

The stationary wave produced on a string is represented by the equation y = 5 cos$\left( \frac{\pi x}{3} \right)\sin(40\pi t)$ where x and y are in cm and t is in seconds. The distance between consecutive nodes is

• A. 5 cm
• B. $\pi$cm
• C. 3 cm
• D. 40 cm

Answer 1

Answer: (C)

3 cm

Answer 2

By comparing with standard equation of stationary wave

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

We get $\frac{2\pi x}{\lambda}$= $\frac{\pi x}{3}$⇒ $\lambda$ = 6; Distance between two consecutive nodes = $\frac{\lambda}{2} = 3cm$