Question

A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz. (a) What could be the maximum value of the fundamental frequency? (b) If transverse waves can travel on this string at a speed of 40 m s⁻¹, what is its length?

Answer 1

Given:
Wire makes a resonant frequency of 240 Hz and 320 Hz when its both ends are fixed.
Therefore, fundamental frequency (f₀) of the wire must be the factor of 240 Hz and 320 Hz.
(a) Maximum value of fundamental frequency, f_{0 =} 80 Hz

(b) Wave speed (v) = 40 m/s
And if $\lambda \mathrm{is}\text{the}\mathrm{wavelength}:$
$\frac{\lambda }{2}=L$

$$\begin{gathered} \therefore v=\lambda \times f_{\mathit{0}} \\ \Rightarrow v=\mathit{2}\times L\times f_{\mathit{0}} \\ \Rightarrow L=\frac{40}{2\times 80} \\ \Rightarrow L=\frac{1}{4}\mathrm{m}=0.25\mathrm{m} \end{gathered}$$