Question

The equation of a stationary wave along a stretched string is given by $y=5\sin ⟮\frac{\pi x}{3}⟯\cos \left(40\pi t\right)$. Where $x$ and $y$ are in $cm$ and $t$ is in sec. The separation between two adjacent nodes is:

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

Answer 1

The correct option is B $1.5cm$

On comparing the given equation with standard equation

$y=2a\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi vt}{\lambda }$

we get

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

Separation between two adjacent nodes is

$\frac{\lambda }{2}=\frac{3}{2}=1.5cm$