Wave Reflection at Free End – Rankers Physics

Standing Wave in String and Organ Pipe: Practice Problem & Solution

Assertion (A): When a pulse on string reflects from free end, the resultant pulse is formed in such a way that slope of string at free end is zero. Reason (R): Zero resultant slope ensures that there is no force component perpendicular to string.  
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 Explained:

To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:

At a free end, there's no transverse force, so the slope \( \frac{\text{dy}}{\text{dx}} = 0 \). The resultant pulse is formed such that the free end is a displacement antinode. This implies zero slope, ensuring no transverse force. Both Assertion and Reason are true, and R correctly explains A.

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