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Tension in a string from a wave equation and the mass per unit length

This type of question, asked 4 times: 15 May 2023 S2, 21 Apr 2025 S2, 20 Apr 2026 S2, 15 May 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    15 May 2023 S2

    49
    A string has mass per unit length of 10−6 kg/cm10^{-6}\text{ kg/cm}. The equation of simple harmonic wave produced in it is Y=0.2sin⁡(2x+80t)Y = 0.2\sin(2x + 80t) m. The tension in the string is

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  2. Question 2

    21 Apr 2025 S2

    33
    A transverse displacement of a vibrating string is y=0.06sin⁡(2πx3)cos⁡(120πt)y = 0.06\sin\left(\frac{2\pi x}{3}\right)\cos(120\pi t). If the mass per unit length of the string is 4×10−24 \times 10^{-2} kg/m, then the tension in the string will be

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  3. Question 3

    20 Apr 2026 S2

    124
    The equation of a wave on a string of linear mass density 0.02 kg m−10.02\ \mathrm{kg\,m^{-1}} is Y=0.01sin⁡[2π(t0.02−x0.50)]Y = 0.01\sin\left[2\pi\left(\dfrac{t}{0.02} - \dfrac{x}{0.50}\right)\right] m. The tension in the string is

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  4. Question 4

    15 May 2026 S1

    121
    A transverse wave is propagating on the string. The linear density of vibrating string is 10−310^{-3} kg/m. The equation of the wave is Y=0.05sin⁡(x+15t)Y = 0.05\sin(x + 15t) where xx and YY are in metre and time in second. The tension in the string is

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