Calculate the frequency of the second harmonic formed on a string of length 0.5 m and mass 2 $\times$ 10^–4 kg when stretched with a tension of 20 N

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744.2 Hz

447.2 Hz

274.4 Hz

44.72 Hz

answer is D.

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Detailed Solution

Mass per unit length $m = \frac{2 \times 10^{- 4}}{0 .5} kg / m = 4 \times 10^{- 4} kg / m$
Frequency of 2^nd harmonic $n_{2} = 2 n_{1}$
$= 2 \times \frac{1}{2 l} \sqrt{\frac{T}{m}} = \frac{1}{0 .5} \sqrt{\frac{20}{4 \times 10^{- 4}}} = 447 .2 Hz$

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