Q: A wire having a linear mass density 5.0 × 10^{-3} kg/m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.

Sol: Suppose the wire vibrates at 420 Hz in its nth harmonic and at 490 Hz in its (p +1)th harmonic.

$\large \frac{490}{420} = \frac{p+1}{p}$

or , p = 6

$\large 420 = \frac{6}{2l} \sqrt{\frac{450}{5\times 10^{-3}}}$

l = 2.1 m