Question

A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50Hz$. The mass of the wire is $30g$ and its lines density is $4\times {10}^{-2}kgm{s}^{-1}$. The speed of the transverse wave in the string is:

• A. $25m{s}^{-1}$
• B. $50m{s}^{-1}$
• C. $75m{s}^{-1}$
• D. $100m{s}^{-1}$

Answer 1

The correct option is C $75m{s}^{-1}$

Here, mass of the wire, $M=30g\times {10}^{-3}kg$
Mass per unit length of the wire,$\mu =4\times {10}^{-2}kgm-1$
$\therefore$ length of the wire,
$L=\frac{M}{\mu }=\frac{30\times {10}^{-3}kg}{4\times {10}^{-2}kg{m}^{-1}}=0.75m$
For the fundamental mode,
$\lambda =2L=2\times 0.75m=1.5m$
Speed of the transverse wave,
$\nu =\upsilon \lambda =\left(50s^{-1}\right)\left(1.5m\right)=75m{s}^{-1}$