A composite string is made up by joining two strings of different masses per unit length μ and 4μ respectively. The composite string is under the same tension. A transverse wave pulse Y = (6 mm) sin (5t + 40x), where t is in seconds and x in metres, is sent along the lighter string towards the joint. The joint is at x = 0. The equation of the wave pulse reflected from the joint is
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Question

A composite string is made up by joining two strings of different masses per unit length μ and 4μ respectively. The composite string is under the same tension. A transverse wave pulse Y = (6 mm) sin (5t + 40x), where t is in seconds and x in metres, is sent along the lighter string towards the joint. The joint is at x = 0. The equation of the wave pulse reflected from the joint is

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G1 Physics · Accepted Answer

Step 1: Compare with y = A sin(ωt ± kx + φ): f = ω/(2π), λ = 2π/k and wave speed v = ω/k. Step 2: The sign of kx fixes the propagation direction; particle motion follows ∂y/∂t. Step 3: Apply these to the given coefficients. Final: C: −(2 mm) sin(5t − 40x).