Question

in a laboratory experiment on standing waves a string 3ft long is attached to the prong of an electrically driven tuning fork which vibrates perpendicular to the length of the string at a frequency of 60vib/sec. the weight of string is0.096lb

(a)what tension the string be under if it is to vibrate four loops

(b)what would happen if the tuning fork is turned so as to vibrate parallel to the length of the string?

Answer 1

a) The string makes four loops. So the wavelength of the vibration,
$\lambda =\frac{3}{2}=1.5ft$
The speed of transverse wave along the string,
$v=\lambda f=1.5\times 60=90ft/s$
Now,
$$\begin{gathered} v=\sqrt{\frac{T}{\mu }} \\ \Rightarrow T=v^2\mu =v^2\frac{m}{L} \\ \Rightarrow T={90}^2\times \frac{0.096}{3}=259.2poundal \end{gathered}$$
b) If the tuning fork is turned it does not change the frequency of vibration. So noting changes.