Duration: 4:40

0 views

0

Consider a standing wave formed on a string. It results due to the superposition of two waves travelling in opposite directions. The waves are travelling along the length of the string in the \( x \)-direction and displacements of elements on the string are along the \( y \)-direction. Individual equations of the two waves can be expressed as
\[
\begin{array}{l}
Y_{1}=6(\mathrm{~cm}) \sin [5(\mathrm{rad} / \mathrm{cm}) x-4(\mathrm{rad} / \mathrm{s}) t] \\
Y_{2}=6(\mathrm{~cm}) \sin [5(\mathrm{rad} / \mathrm{cm}) x+4(\mathrm{rad} / \mathrm{s}) t]
\end{array}
\]
Here \( x \) and \( y \) are is \( \mathrm{cm} \).
If one end of the string is at \( x=0 \), positions of the nodes can be described as
(1) \( x=n \pi / 5 \mathrm{~cm} \), where \( n=0,1,2, \ldots \)
(2) \( x=n 2 \pi / 5 \mathrm{~cm} \), where \( n=0,1,2, \ldots \)
(3) \( x=n \pi / 5 \mathrm{~cm} \), where \( n=1,3,5, \ldots \)
(4) \( x=n \pi / 10 \mathrm{~cm} \), where \( n=1,3,5, \ldots \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live