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  4. The wave - function for a certain standing wave on a string fixed at both ends is y(x , t)=0.5sin(0 . 025 π x)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:-

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Q. 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:-

NTA AbhyasNTA Abhyas 2022

Solution:

$K=\frac{2 \pi }{\lambda }=0.025\pi \Rightarrow \frac{\lambda }{2}=\frac{1}{0 . 025}=40cm$
The shortest possible length will be
$L_{min}=\frac{\lambda }{2}=40cm$