Question

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

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

Answer 1

The Correct Option is C

Here, Mass of the wire, $M=30\,g =30 \times 10^{-3}\, kg$ Mass per unit length of the wire, $\mu=4\times10^{-2} \, kg\, m^{-1}$ $\therefore$ Length of the wire, $L=\frac{M}{\mu}=\frac{30\times10^{-3}\,kg}{4\times10^{-2}\,kg\,m^{-1}} =0.75\,m$

For the fundamental mode, $\lambda=2L=2\times0.75\,m=1.5\,m$ Speed of the transverse wave, $v=\upsilon\lambda=\left(50\,s^{-1}\right)\left(1.5\,m\right)$ $=75\,m\,s^{-1}$