A uniform string of length L and total mass M is suspended vertically and a transverse pulse is given at the top end of it. At the same moment a body is released from rest and falls freely from the top of the string. How far from the bottom does the body pass the pulse?
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Question

A uniform string of length L and total mass M is suspended vertically and a transverse pulse is given at the top end of it. At the same moment a body is released from rest and falls freely from the top of the string. How far from the bottom does the body pass the pulse?

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G1 Physics · Accepted Answer

Step 1: Local transverse-wave speed is v = √(T/μ). Step 2: If T varies with position, use dt = dx/v and integrate; otherwise use time = length/speed. Step 3: Use force balance to obtain the required tension where needed. Final: A: L/9.