Question

A stretched string of mass 20 g vibrates with a frequency of 30 Hz in its fundamental
mode and the supports are 40 cm apart. The amplitude of vibrations at the antinode is
4 cm. Calculate the velocity of propagation of the wave in the string as well as the tension
in it.

Answer 1

A stretched string of mass $20\,\mathrm{g}$ vibrates with a frequency of $30\,\mathrm{Hz}$ in its fundamental mode and the supports are $40\,\mathrm{cm}$ apart. The amplitude of vibrations at the antinode is $4\,\mathrm{cm}$. Calculate the velocity of propagation of the wave in the string as well as the tension in it.

Solution

$$v = f \lambda = f 2 l = 3 0 * 2 * 4 0 * 0. 0 1 = 2 4 \frac {\mathrm {m}}{\mathrm {s}}$$

To obtain the tension is a bit more complicated because it appears

within a square root:

$$v = \sqrt {\frac {T}{\mu}} \gg T = \mu v ^ {2} = \frac {m}{l} v ^ {2} = \frac {2 0 * 0 . 0 0 1}{4 0 * 0 . 0 1} 2 4 ^ {2} = 2 8, 8 \mathrm {N}$$