Question

In an experiment of standing waves, a string 90 cm long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string at a frequency of 60 Hz. The mass of the string is 0.044 kg. What tension must the string be under (weights are attached to the other end) if it is to oscillate in four loops?

Answer 1

we know $\lambda =\frac{2L}{n}$

here $L=0.9m$ and $n=4$

so $\lambda =\frac{2\times 0.9}{4}=0.45cm$

we also know that $v=f\lambda =60\times 0.45=27m/s$

and $\mu =0.044/0.9=0.49kg/m$

so $v=\sqrt{T/\mu }⟹T=v^2\mu$

$T={27}^2\times 0.049=36N$