Question

The equation of a standing wave produced on a string fixed at both the ends is $y=0.4\sin \left(0.314x\right)\cos \left(600\pi t\right)$, where $x$ is in $\text{cm}$, $t$ is in seconds. The smallest possible length of the string would be

• A. $20\text{cm}$
• B. $40\text{cm}$
• C. $10\text{cm}$
• D. None of these

Answer 1

The correct option is C $10\text{cm}$

From the given equation of standing wave,
$\lambda =\frac{2\pi }{k}=\frac{2\pi }{0.314}=20\text{cm}$


For the smallest length of string, one loop is produced (fundamental mode).
i.e $d=\frac{\lambda }{2}=10\text{cm}$