A wire having a linear mass density 9.0 × 10^-4 kg/m is stretched between two rigid supports with a tension of 900 N. The wire resonates at a frequency of 500 Hz. The next higher frequency at with the same wire resonates is 550 Hz. The length of the wire is______m.

$\mu =9\times 10^{-4}kg/m$

T = 900 N

$f_0=500Hz\to$ resonance frequency

$f_0^{\text{'}}=550Hz\to$ Next higher frequency

$v=\sqrt[]{\frac{T}{\mu }}=\sqrt[]{\frac{900N}{9\times 10^{-4}}}=1000m/s$

$\therefore 500Hz=\frac{10\times 1000}{2\times \mathcal{l}}$

$\mathcal{l}=10m$

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