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
$y=2 a \sin \frac{2 \pi}{\lambda} x \cos \frac{2 \pi}{\lambda} c t \ldots(1)$
Where $a$ is amplitude, $\lambda$ is wavelength.
Given equation is
$y=5 \sin \frac{\pi x}{3} \cos 40 \pi t \ldots(2)$
Comparing Eqs. (1) and (2), we get
$\frac{2 \pi}{\lambda}=\frac{\pi}{3}$
$\Rightarrow \lambda=6 cm$
Distance between adjacent nodes
$=\frac{\lambda}{2}=\frac{6}{2}$
$=3 \,cm$