Question

The equation of a stationary wave is $y=\sin \frac{\pi x}{3}\cos 10\pi t$ where $x$ and $y$ are in centimeters and $t$ in seconds. The separation between two consecutive nodes is

• A. $1.5cm$
• B. $6.0cm$
• C. $3.0cm$
• D. $18cm$

Answer 1

Answer: (C)

$3.0cm$

Comparing the given equation with standard stationary wave equation, we get $k=\frac{\pi }{3}=\frac{2\pi }{\lambda }\Rightarrow \lambda =6$ cm.
Hence, the separation between two consecutive nodes $=\frac{\lambda }{2}=3$ cm.