Question Detail
Question
A vibrating string is described by the equation y = 0.5sin(2x−3t), where x and y are in metres and t in seconds. If the tension in the string is 0.4 N, what is the linear density (mass per unit length) of the string?
Correct Answer
Option B is the correct answer.
Detailed Explanation
The general wave equation is y = A sin(kx - ωt). From the given equation, k = 2 rad/m and ω = 3 rad/s.The wave speed v = ω/k = 3/2 = 1.5 m/s.For a wave on a string, the speed is also given by v = √(F/μ), where F is the tension and μ is the linear density.Rearranging for μ: μ = F / v².μ = 0.4 N / (1.5 m/s)² = 0.4 / 2.25 = 8/45 kg/m ≈ 0.1778 kg/m.
Hint
Extract the wave number (k) and angular frequency (ω) from the wave equation to find the wave speed (v). Then use the formula for wave speed on a string relating tension and linear density.