Question

The wave - function for a certain standing wave on a string fixed at both ends is $y\left(x,t\right)=0.5sin\left(0.025\pi x\right)cos500t$ where $x$ and $y$ are in centimetres and $t$ is in seconds. the shortest possible length of the string is $8n$ then $n$ is:-

Answer 1

Answer: 5

$K=\frac{2\pi }{\lambda }=0.025\pi \Rightarrow \frac{\lambda }{2}=\frac{1}{0.025}=40cm$
The shortest possible length will be
$L_{min}=\frac{\lambda }{2}=40cm$