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

Wave Speed Formula:
$v = f \lambda$

Calculate the velocity of propagation of the wave in the string.
Let L be the length of string.

$v = f \lambda = f2L = 30Hz \cdotp 2\cdotp0.4m = 24m/s$

the tension:

We know,

$v = \sqrt{ \frac{T}{\mu} }$
Then, $v^2 = \frac{T}{\mu}$

So,
$T = v^2\mu = v^2ML = 24m/s^2 \cdotp \frac{0.02 kg}{0.4m} = 28.8 N$