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  4. A uniform wire of linear density 0.004 kg - m -1 when stretched between two rigid supports with a tension 3.6 × 102 N, resonates with a frequency of 420 Hz. The next harmonic frequency with which the wire resonates is 490 Hz. The length of the wire in metres is

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Q. A uniform wire of linear density $0.004 \,kg - m ^{-1}$ when stretched between two rigid supports with a tension $3.6 \times 10^{2} \,N$, resonates with a frequency of $420 \,Hz$. The next harmonic frequency with which the wire resonates is $490 \,Hz$. The length of the wire in metres is

Punjab PMETPunjab PMET 2008Electromagnetic Waves

Solution:

$\therefore n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$
or $490-420 =\frac{1}{2 \times l} \sqrt{\frac{3.6 \times 10^{2}}{0.004}}$
or $70 =\frac{1}{2 l} \times 300 $
or $l =\frac{300}{2 \times 70} $
$=2.14\, m$