Question

The linear density of a vibrating string is 1.3 × 104 kg m1. A transverse wave is propagating on the string and is described by the equation y (x, t) = 0.021 sin (30t x) where x and y are in metres and t is in seconds. Calculate the tension in the string.

Answer 1

Answer on Question #65639, Physics / Mechanics | Relativity

The linear density of a vibrating string is $1.3 \times 10^{-4} \, \mathrm{kg} \, \mathrm{m}^{-1}$. A transverse wave is propagating on the string and is described by the equation $y(x, t) = 0.021 \sin(30t x)$ where $x$ and $y$ are in metres and $t$ is in seconds. Calculate the tension in the string.

Solution:

$$v = f \lambda = \frac{2 \pi \omega}{2 \pi k} = \frac{\omega}{k} = \frac{30}{1} = 30 \, \mathrm{m/s}$$ $$v = \sqrt{\frac{T}{\mu}}$$ $$T = \mu v^2$$ $$T = 1.3 \cdot 10^{-4} \times 30^2 = 0.117 \, \mathrm{N}$$

Answer: 0.117 N

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