A uniform wire of linear density 0.004 Kgm-1 when stretched between two rigid support with a tension 3.6 ×102 N resonates with a frequency of 420Hz. The next harmonic frequency with which wire resonates is 490 Hz. The length of the wire (in metre is)

A s frequency of nth harmonic and (n+1)th harmonic has difference given asn+12LTμ−n2LTμ=12LTμ490−420=12L3.6×1020.00470=12L×300→L=3002×70=2.14m

A uniform wire of linear density 0.004 Kgm-1 when stretched between two rigid support with a tension 3.6 ×102 N resonates with a frequency of 420Hz. The next harmonic frequency with which wire resonates is 490 Hz. The length of the wire (in metre is)

A s frequency of nth harmonic and (n+1)th harmonic has difference given asn+12LTμ−n2LTμ=12LTμ490−420=12L3.6×1020.00470=12L×300→L=3002×70=2.14m

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A uniform wire of linear density $0.004 K g m^{- 1}$ when stretched between two rigid support with a tension $3.6 \times 10^{2} N$ resonates with a frequency of 420Hz. The next harmonic frequency with which wire resonates is 490 Hz. The length of the wire (in metre is)

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1.41

2.14

2.41

8.14

answer is B.

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Detailed Solution

A s frequency of n^th harmonic and (n+1)^th harmonic has difference given as

$\frac{n + 1}{2 L} \sqrt{\frac{T}{μ}} - \frac{n}{2 L} \sqrt{\frac{T}{μ}} = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$

$490 - 420 = \frac{1}{2 L} \sqrt{\frac{3.6 \times 10^{2}}{0.004}}$

$70 = \frac{1}{2 L} \times 300 \to L = \frac{300}{2 \times 70} = 2.14 m$

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A uniform wire of linear density 0.004 Kgm-1 when stretched between two rigid support with a tension 3.6 ×102 N resonates with a frequency of 420Hz. The next harmonic frequency with which wire resonates is 490 Hz. The length of the wire (in metre is)

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A uniform wire of linear density $0.004 K g m^{- 1}$ when stretched between two rigid support with a tension $3.6 \times 10^{2} N$ resonates with a frequency of 420Hz. The next harmonic frequency with which wire resonates is 490 Hz. The length of the wire (in metre is)