Question

A long string is moved up and down with simple harmonic motion with a frequency of 46 Hz. The string is 579 m long and has a total mass of 46.3 kg. The string is under a tension of 3423 and is fixed at both ends. Determine the velocity of the wave on the string. What length of the string, fixed at both ends, would create a third harmonic standing wave

Answer 1

Answer:

a)  $v=206.896m/s$

b)  $L=6.749m$

Explanation:

From the question we are told that:

Frequency $F=46Hz$

Length $l=579m$

Total Mass $T=4.3kg$

Tension $T=3423$

a)

Generally the equation for velocity is mathematically given by

$v=\sqrt{\frac{T}{\rho}}$

Where

$\pho=m*l\\\\\pho=46*579\\\\\pho=0.0799kg/m$

Therefore

$v=\sqrt{\frac{3423}{0.0799}}$

$v=206.896m/s$

b)

Generally the equation for length of string is mathematically given by

$L=\frac{3\lambda}{2}$

Where

$\lambda=\frac{v}{f}$

$\lambda=\frac{206.89}{46}$

$\lambda=4.498$

Therefore

$L=\frac{3*4.498}{2}$

$L=6.749m$