Question 491: Waves

Question

A steel wire of mass 4 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N , then the frequency of fourth harmonic is

Accepted Answer

For transverse wave in string,
$$ m=4 \mathrm{~g}, I=80 \mathrm{~cm}, T=50 \mathrm{~N} $$
Ã¢ÂÂ´ Mass per unit length,
$$ \begin{aligned} \mu & =\frac{m}{l}=\frac{4 	imes 10^{-3}}{80 	imes 10^{-2}} \mathrm{~kg} / \mathrm{m} \ & =5 	imes 10^{-3} \mathrm{~kg} / \mathrm{m} \end{aligned} $$
Ã¢ÂÂ´ The frequency of $n^{	ext {th }}$ harmonic is
$$ f_n=\frac{n}{2 l} \sqrt{\frac{T}{\mu}} $$
Ã¢ÂÂ´ For $4^{	ext {th }}$ harmonic, $n=4$
$$ \begin{aligned} 	herefore \quad t_4 & =\frac{4}{2 	imes 80 	imes 10^{-2}} \sqrt{\frac{50}{5 	imes 10^{-3}}} \ & =250 \mathrm{~Hz} \end{aligned} $$

Answer

250 Hz

Answer

500 Hz

Answer

700 Hz

Answer

1000 Hz

Waves

A steel wire of mass 4 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N , then the frequency of fourth harmonic is

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