Question

A steel wire has a length of $90\, cm$ which is under a constant tension of $100\, N$. The speed of the transverse waves that can be produced in the wire will be (take the mass of the steel Wire to be $6 \times 10^{-3} \, kg$)

• A. $ 50 \, m / s$
• B. $ 50 \, cm / s$
• C. $ 1 / 3\sqrt{6} \, m / s$
• D. $50\sqrt{6} \, m / s$

Answer 1

Answer: (D)

Speed of transver~e wave, $v = \sqrt{\frac{T}{\mu}}$
Here, $T = 100\, N, m = 6 \times 10^{-3}\, kg$
$I= 90 \,cm = 0.9 \, m$
$\mu =\frac{m}{l} =\frac{6\times10^{-3}}{0.9} =\frac{6}{9} \times10^{-2}\, kg \, m^{-1}$
$v = \sqrt{\frac{100}{\frac{6}{9} \times10^{-2}}} =\sqrt{\frac{9}{6} \times10^{4}} $
$ = 50\sqrt{6} \, m \, s^{-1} $