Physics - Wave on String Question with Solution | TestHub

The given equation of the stationary wave is $y=5\sin \left(\frac{\pi x}{3}\right)\cos (40\pi t)$.

Comparing this with the standard equation of a stationary wave $y=A\sin (kx)\cos (\omega t)$, we get the wave number $k=\frac{\pi }{3}$.

Since $k=\frac{2\pi }{\lambda }$, we have:

$\frac{2\pi }{\lambda }=\frac{\pi }{3}$

$\lambda =6$ cm

The separation between two adjacent nodes in a stationary wave is $\frac{\lambda }{2}$.

Separation = $\frac{6}{2}=3$ cm.

Answer: $3$ cm