A nonuniform rope of length ℓ hangs from a ceiling. Its linear mass density varies as μ = μ₀eʸ, where y is measured from the lower end. Which graph best represents v² versus y?

Question

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: Image 1.