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 centimeter and $t$ in second. The separation between two adjacent nodes is:

• A. 6 cm
• B. 4 cm
• C. 3 cm
• D. 1.5 cm

Answer 1

Answer: (C)

Distance between adjacent nodes in half of wavelength.
The standard equation of stationary wave is
$y=2a\sin \frac{2\pi }{\lambda }x\cos \frac{2\pi }{\lambda }ct\dots (1)$
Where $a$ is amplitude, $\lambda$ is wavelength.
Given equation is
$y=5\sin \frac{\pi x}{3}\cos 40\pi t\dots (2)$
Comparing Eqs. (1) and (2), we get
$\frac{2\pi }{\lambda }=\frac{\pi }{3}$
$\Rightarrow \lambda =6cm$
Distance between adjacent nodes
$=\frac{\lambda }{2}=\frac{6}{2}$
$=3cm$