Question

A string of length $L$ is taut between two cliffs. It is clamped at length $\frac{L}{8}$. If a standing wave is formed on this string, what will be the maximum wavelength of the wave?

• A. $\frac{L}{2}$
• B. $\frac{L}{4}$
• C. $\frac{L}{8}$
• D. $L$

Answer 1

The correct option is B $\frac{L}{4}$

Since the string is clamped at length $\frac{L}{8}$, so at this point there must be a node.

Since we have to calculate maximum wavelength, we can assume one loop between $0$ and $\frac{L}{8}$.


For formation of one loop, the wavelength of the wave will be $\frac{\lambda }{2}$

$\Rightarrow \frac{\lambda }{2}=\frac{L}{8}$

$\Rightarrow \lambda =\frac{L}{4}$

Hence, option $\left(B\right)$ is correct

Why this question ? This question gives you understanding about formation of standing wave and condition of maximum wavelength.