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

Question

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 (A) 1.41 (B) 2.14 (C) 2.41 (D) 3.14

Tardigrade Admin · Accepted Answer

∴ n=(1/2 l) √(T/m) or 490-420 =(1/2 × l) √(3.6 × 102/0.004) or 70 =(1/2 l) × 300 or l =(300/2 × 70) =2.14 m

Q. A uniform wire of linear density $0.004 k g - m^{- 1}$ when stretched between two rigid supports with a tension $3.6 \times 1 0^{2} N$ , 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

1.41

2.14

2.41

3.14

$∴ n = \frac{1}{2 l} \frac{T}{m}$
or $490 - 420 = \frac{1}{2 \times l} \frac{3.6 \times 1 0 ^{2}}{0.004}$
or $70 = \frac{1}{2 l} \times 300$
or $l = \frac{300}{2 \times 70}$
$= 2.14 m$

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