Question

The linear density of a vibrating string is 1.3 × 10^−4 kg/m. 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 #69153 Physics / Mechanics | Relativity

The linear density of a vibrating string is $\mu = 1.3 \times 10^{\wedge} - 4 \, \mathrm{kg/m}$. 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:

The tension in the string

$$T = \mu v^{2}$$

where $v$ is the velocity of propagation of a wave in a string.

Because wave is described by the equation

$$y(x,t) = 0.021 \sin(30t - x) = A \sin(\omega t - kx)$$

velocity is

$$v = \frac{\omega}{k} = \frac{30}{1} = 30 \, \frac{\mathrm{m}}{\mathrm{s}}.$$

Thus

$$T = 1.3 \times 10^{-4} \times 30^{2} = 0.117 \, \mathrm{N}.$$

Answers: 0.117 N

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