Question

The equation of stationary wave along a stretched string is given by $y=5\, \sin \frac{\pi x}{3} \cos 40\, \pi t$, where, $x$ and $y$ are in $cm$ and $t$ in second. The separation between two adjacent nodes is :

• A. 1. 5 cm
• B. 3 cm
• C. 6 cm
• D. 4 cm

Answer 1

Answer: (B)

3 cm

Answer 2

Given, equation
$y=5\, \sin \frac{\pi x}{3} \cos 40 \pi t$
Comparing with standard equation
$y=A \sin k x \cos \omega t$
$\therefore k =\frac{\pi}{3}$
$\Rightarrow \frac{2 \pi}{\lambda} =\frac{\pi}{3}$
$\lambda =6\, cm$
Separation between two consecutive nodes
$=\frac{\lambda}{2}=\frac{6}{2}=3\, cm$