A long string under tension 100 N has one end at x = 0. A wave is generated there: y = (0.01 cm) sin[(πx/10 m) - 50πt], with t in seconds. (i) Sketch the string at t = 1/50 s. (ii) Find the average power transmitted. (iii) Draw the particle-velocity versus time graph at x = 5 m. Image
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Question

A long string under tension 100 N has one end at x = 0. A wave is generated there: y = (0.01 cm) sin[(πx/10 m) - 50πt], with t in seconds. (i) Sketch the string at t = 1/50 s. (ii) Find the average power transmitted. (iii) Draw the particle-velocity versus time graph at x = 5 m. Image

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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: D: (i) required waveform as in source; (ii) 25 × 10⁻⁶ W; (iii) corresponding velocity-time graph.

A long string under tension 100 N has one end at x = 0. A wave is generated there: y = (0.01 cm) sin[(πx/10 m) − 50πt], with t in seconds. (i) Sketch the string at t = 1/50 s. (ii) Find the average power transmitted. (iii) Draw the particle-velocity versus time graph at x = 5 m. Image