Question

The equation of a stationary wave is given by $y=6\sin \left(\frac{\pi x}{3}\right)\cos 40\pi t$ where $y$ and $x$ are given in $cm$ and time $t$ in second. Then the separation between two consecutive antinodes is:

• A. $20cm$
• B. $6cm$
• C. $3cm$
• D. $12cm$

Answer 1

The correct option is C $3cm$

Given,
$y=6\sin \left(\frac{\pi x}{3}\right)\cos 40\pi t$
Comparing it with the standard form
i.e.
$y=2a\sin kx\cos \omega t$
$k=\frac{\pi }{3}$
$\because k=\frac{2\pi }{\lambda }$
$\left(\frac{2\pi }{\lambda }\right)=\frac{\pi }{3}$
or $\lambda =6cm$
Separation between two consecutive antinodes,
$D=\frac{\lambda }{2}=\frac{6}{2}=3cm$

Final answer: (a)