A transverse wave given by y = (0.02 m ) [(1.0 m ⁻¹)x + (30 s ⁻¹)t] propagates along a stretched string with a linear mass density of 1.2 10⁻⁴ kg m ⁻¹ . Determine the tension in the string.

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Correct answer: A. 0.108 N

Comparing the given equation y = 0.02 (x + 30t) with the standard wave equation y = A (kx + t) , we get: k = 1.0 m ⁻¹ = 30 s ⁻¹ The wave speed v is given by: v = k = 30 1.0 = 30 m s ⁻¹ The wave speed on a stretched string is related to tension T and linear mass density by: v = T T = v^2 Given = 1.2 10⁻⁴ kg m ⁻¹ , substituting the values: T = (1.2 10⁻⁴) (30)^2 T = 1.2 10⁻⁴ 900 T = 1080 10⁻⁴ = 0.108 N

A transverse wave given by y = (0.02 m ) [(1.0 m ⁻¹)x + (30 s ⁻¹)t] propagates along a stretched string with a linear mass density of 1.2 10⁻⁴ kg m ⁻¹ . Determine the tension in the string.

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