A wave of frequency $100\text{ Hz}$ is sent along a string towards a fixed end. When this wave travels back…
A wave of frequency $100\text{ Hz}$ is sent along a string towards a fixed end. When this wave travels back after reflection, a node is formed at a distance of $10\text{ cm}$ from the fixed end of the string. The speed of incident wave is
(a) $48\text{ ms}^{-1}$
(b) $20\text{ ms}^{-1}$
(c) $10\text{ ms}^{-1}$
(d) $15\text{ ms}^{-1}$
Solution
Here, $\frac{\lambda}{2} = 10\text{ cm} = 0.1\text{ m} \Rightarrow \lambda = 0.2\text{ m}$
[Diagram shows a standing wave loop of length $\lambda/2$ with frequency $f = 100\text{ Hz}$ between two nodes $N$.]
Now, speed of incident wave, $v = f \lambda = 20\text{ ms}^{-1}$