Normal Modes of Stretched String – Rankers Physics
Topic: Waves
Subtopic: Standing Wave in String and Organ Pipe

Normal Modes of Stretched String

Assertion (A): In \(n^{\text{th}}\) normal mode of a stretched string, there are \(n\) antinodes and \((n+1)\) nodes.
Reason (R): The ends of string are nodes, so the number of nodes is one more than the number of antinodes.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true. For a stretched string fixed at both ends, the \(n^{\text{th}}\) normal mode indeed has \(n\) antinodes and \(n+1\) nodes.


Reason (R) is true and correctly explains this: the fixed ends are always nodes, leading to one more node than antinode.

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