Question

What are (a) the lowest frequency, (b) the second lowest frequency, and (c) the third lowest frequency for standing waves on a wire that is $10.0$m long has a mass of $100$g, and is stretched under a tension of $250$N?

Answer 1

Mass per unit length of the wire $\mu =\frac{M}{L}=\frac{0.1}{10}=0.01kg/m$

Tension $T=250N$

Velocity of standing waves $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{250}{0.01}}=158m/s$

(a) : Lowest frequency ${\nu }_o=\frac{v}{2L}=\frac{158}{2\times 10}=7.9Hz$

(b) : Second lowest frequency ${\nu }_2=2{\nu }_o=2\times 7.9=15.8Hz$

(c) : Third lowest frequency ${\nu }_3=3{\nu }_o=3\times 7.9=23.7Hz$